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Mathematics > 1.3 Prime numbers > Flashcards

1.3 Prime numbers Flashcards

1
Q

What are multiples of a number?

A

Multiples are the results of multiplying a number by positive integers.

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2
Q

How can you think of multiples of a number?

A

As the ‘times table’ for that number.

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3
Q

What is an example of multiples of 3?

A

3 × 1 = 3, 3 × 2 = 6, 3 × 3 = 9, and so on.

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4
Q

How is the first multiple of any number found?

A

It is the number itself (the number multiplied by 1).

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5
Q

List the first five multiples of 2.

A

2, 4, 6, 8, 10

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6
Q

List the first five multiples of 3.

A

3, 6, 9, 12, 15

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7
Q

List the first five multiples of 5.

A

5, 10, 15, 20, 25

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8
Q

List the first five multiples of 8.

A

8, 16, 24, 32, 40

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9
Q

List the first five multiples of 9.

A

9, 18, 27, 36, 45

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10
Q

List the first five multiples of 10.

A

10, 20, 30, 40, 50

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11
Q

List the first five multiples of 12.

A

12, 24, 36, 48, 60

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12
Q

List the first five multiples of 100.

A

100, 200, 300, 400, 500

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13
Q

Use a calculator to find the first ten multiples of 29.

A

29, 58, 87, 116, 145, 174, 203, 232, 261, 290

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14
Q

Use a calculator to find the first ten multiples of 44.

A

44, 88, 132, 176, 220, 264, 308, 352, 396, 440

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15
Q

Use a calculator to find the first ten multiples of 75.

A

75, 150, 225, 300, 375, 450, 525, 600, 675, 750

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16
Q

Use a calculator to find the first ten multiples of 114.

A

114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140

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17
Q

List the multiples of 4 between 29 and 53.

A

32, 36, 40, 44, 48, 52

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18
Q

List the multiples of 50 less than 400.

A

50, 100, 150, 200, 250, 300, 350

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19
Q

List the multiples of 100 between 4000 and 5000.

A

4100, 4200, 4300, 4400, 4500, 4600, 4700, 4800, 4900

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20
Q

Which of these numbers are multiples of 12: 576, 396, 354, 792, 1164?

A

576, 396, 792, 1164

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21
Q

Which of the following numbers are NOT multiples of 27: 324, 783, 816, 837, 1116?

A

816

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22
Q

What is the lowest common multiple (LCM)?

A

The smallest number that is a multiple of all the given numbers.

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22
Q

What is the first step to find the LCM of two numbers?

A

Find the prime factorization of both numbers.

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23
Q

What do you do after finding the prime factorization of the numbers?

A

List the prime factors, taking the highest power of each factor that appears.

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24
Q

What do you do with the prime factors to find the LCM?

A

Multiply the highest powers of all prime factors together.

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25
Q

What is an example of finding the LCM for 12 and 18?

A

Prime factors of 12: 2^2 × 3
Prime factors of 18: 2 × 3^2
LCM: 2^2 × 3^2 = 36.**

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26
Q

What’s a shortcut to find the LCM for smaller numbers?

A

Write out the multiples of each number and find the smallest common one.

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27
Q

What is the LCM of 4 and 6 using multiples?

A

Multiples of 4: 4, 8, 12, 16…
Multiples of 6: 6, 12, 18, 24…
LCM: 12

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28
Q

What does the LCM help with in math?

A

It is useful for adding or subtracting fractions and solving problems involving repeated patterns.

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29
Q

Find the LCM of 2 and 5.

A

LCM = 10

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30
Q

Find the LCM of 8 and 10.

A

LCM = 40

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31
Q

Find the LCM of 6 and 4.

A

LCM = 12

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32
Q

Find the LCM of 3 and 9.

A

LCM = 9

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33
Q

Find the LCM of 35 and 55.

A

LCM = 385

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34
Q

Find the LCM of 6 and 11.

A

LCM = 66

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35
Q

Find the LCM of 2, 4, and 8.

A

LCM = 8

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36
Q

Find the LCM of 4, 5, and 6.

A

LCM = 60

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37
Q

Find the LCM of 6, 8, and 9.

A

LCM = 72

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38
Q

Find the LCM of 1, 3, and 7.

A

LCM = 21

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39
Q

Find the LCM of 4, 5, and 8.

A

LCM = 40

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40
Q

Find the LCM of 3, 4, and 18.

A

LCM = 36

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41
Q

Is it possible to find the highest common multiple of two or more numbers?

A

No, because there is no highest common multiple. The multiples continue infinitely.

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42
Q

What is a factor?

A

A factor is a number that divides exactly into another number with no remainder.

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43
Q

What is the largest factor of any number?

A

The largest factor of any number is the number itself.

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44
Q

How do you list factors in numerical order?

A

Go down the left side and then up the right side of the factor pairs, remembering not to repeat factors.

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45
Q

Find the factors of 12.

A

Factors of 12 = 1, 2, 3, 4, 6, 12
(Factor pairs: 1 × 12, 2 × 6, 3 × 4)

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46
Q

Find the factors of 25.

A

Factors of 25 = 1, 5, 25
(Factor pair: 1 × 25, 5 × 5)

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47
Q

Find the factors of 110.

A

Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110
(Factor pairs: 1 × 110, 2 × 55, 5 × 22, 10 × 11)

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48
Q

List all the factors of 4.

A

Factors of 4 = 1, 2, 4

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49
Q

List all the factors of 5.

A

Factors of 5 = 1, 5

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50
Q

List all the factors of 8.

A

Factors of 8 = 1, 2, 4, 8

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51
Q

List all the factors of 11.

A

Factors of 11 = 1, 11

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52
Q

List all the factors of 18.

A

Factors of 18 = 1, 2, 3, 6, 9, 18

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53
Q

List all the factors of 12.

A

Factors of 12 = 1, 2, 3, 4, 6, 12

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54
Q

List all the factors of 35.

A

Factors of 35 = 1, 5, 7, 35

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55
Q

List all the factors of 40.

A

Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40

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56
Q

List all the factors of 57.

A

Factors of 57 = 1, 3, 19, 57

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57
Q

List all the factors of 90.

A

Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

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58
Q

List all the factors of 100.

A

Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100

59
Q

List all the factors of 132.

A

Factors of 132 = 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

60
Q

List all the factors of 160.

A

Factors of 160 = 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

61
Q

List all the factors of 153.

A

Factors of 153 = 1, 3, 9, 17, 51, 153

62
Q

List all the factors of 360.

A

Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

63
Q

True or false: 3 is a factor of 313.

A

False

64
Q

True or false: 9 is a factor of 99.

A

True

65
Q

True or false: 3 is a factor of 300.

A

True

66
Q

True or false: 2 is a factor of 300.

A

True

67
Q

True or false: 2 is a factor of 122488.

A

True

68
Q

True or false: 12 is a factor of 60.

A

True

69
Q

True or false: 210 is a factor of 210.

A

True

70
Q

True or false: 8 is a factor of 420.

A

True

71
Q

What is the smallest factor and the largest factor of any number?

A

The smallest factor is 1, and the largest factor is the number itself.

72
Q

How do you find the HCF of two numbers?

A

List the factors of each number, underline the common factors, and pick the highest underlined factor as the HCF.

73
Q

Find the HCF of 8 and 24.

A

Factors of 8 = 1, 2, 4, 8; Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
HCF = 8

74
Q

What is the HCF of 3 and 6?

A

HCF = 3

75
Q

What is the HCF of 24 and 16?

A

HCF = 8

76
Q

What is the HCF of 15 and 40?

A

HCF = 5

77
Q

What is the HCF of 42 and 70?

A

HCF = 14

78
Q

What is the HCF of 32 and 36?

A

HCF = 4

79
Q

What is the HCF of 26 and 36?

A

HCF = 2

80
Q

What is the HCF of 22 and 44?

A

HCF = 22

81
Q

What is the HCF of 42 and 48?

A

HCF = 6

82
Q

Find the HCF of 3, 9, and 15.

A

HCF = 3

83
Q

What is the HCF of two different prime numbers? Why?

A

HCF = 1, because prime numbers have no common factors except 1.

84
Q

Simeon has rope lengths of 72m and 90m. What is the longest equal piece he can cut?

A

HCF = 18 metres.

85
Q

Ms. Sanchez has 40 canvases and 100 tubes of paint. What is the largest number of students she can divide these equally among?

A

HCF = 20 students.

86
Q

Indira has 300 blue beads, 750 red beads, and 900 silver beads. What is the maximum number of bracelets she can make?

A

HCF = 150 bracelets.

87
Q

What is a prime number?

A

A prime number is a number greater than 1 with exactly two factors: 1 and itself.

88
Q

What is the only even prime number?

A

2

89
Q

How can you test if a number is prime?

A

Check if it is divisible by smaller prime numbers up to its square root.

90
Q

Is a number prime if it’s divisible by any number other than 1 and itself?

A

No, it is not prime.

91
Q

What is the square root rule for primes?

A

To check if a number is prime, test divisors only up to its square root.

92
Q

What are the prime numbers less than 30?

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

93
Q

Is 29 a prime number? Why?

A

Yes. It is only divisible by 1 and 29.

94
Q

Why can you stop checking for divisors at the square root of a number?

A

Because any factor larger than the square root would already have a smaller factor pair.

95
Q

Which is the only even prime number?

A

2

96
Q

How many odd prime numbers are there less than 50?

A

15

97
Q

What are composite numbers greater than 4 but less than 30?

A

6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28

98
Q

Write composite numbers 6 and 8 as the sum of two prime numbers.

A

6 = 3 + 3
8 = 3 + 5

99
Q

What are twin primes?

A

Twin primes are pairs of prime numbers that differ by 2.

100
Q

List all twin prime pairs up to 100.

A

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73)

101
Q

Is 149 a prime number?

A

Yes. 149 is prime because it has no factors other than 1 and 149.

102
Q

What is a super-prime number?

A

A prime number that stays prime when digits are removed one by one, starting with the units place.

103
Q

Give two three-digit super-prime numbers less than 400.

A

239 and 359

104
Q

Find a four-digit super-prime number less than 3000.

A

2333

105
Q

Is Sondra’s telephone number 987-6413 a super-prime?

A

No. When digits are removed, it does not remain prime.

106
Q

What are prime factors?

A

Prime factors are the factors of a number that are also prime numbers.

107
Q

How can a composite number be written using prime factors?

A

By expressing it as the product of its prime factors using a factor tree or division method.

108
Q

What are the prime factors of 36?

A

2 × 2 × 3 × 3

109
Q

What are the prime factors of 48?

A

2 × 2 × 2 × 2 × 3

110
Q

What is the HCF of 168 and 180?

A

12 (HCF = 2 × 2 × 3)

111
Q

What is the LCM of 72 and 120?

A

360 (LCM = 2 × 2 × 2 × 3 × 3 × 5)

112
Q

How do you find the HCF using prime factorisation?

A

Express each number as the product of its prime factors, find common factors, and multiply them.

113
Q

How do you find the LCM using prime factorisation?

A

Express each number as the product of its prime factors, take the largest set of multiples for each factor, and multiply them.

114
Q

Which divisibility rule applies to 2?

A

A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.

115
Q

What is the divisibility rule for 3?

A

A number is divisible by 3 if the sum of its digits is a multiple of 3.

116
Q

How do you test if a number is divisible by 4?

A

Check if the last two digits can be divided by 4.

117
Q

What is the rule for divisibility by 5?

A

A number is divisible by 5 if it ends in 0 or 5.

118
Q

What is the divisibility rule for 6?

A

A number is divisible by 6 if it is divisible by both 2 and 3.

119
Q

How do you check divisibility by 8?

A

A number is divisible by 8 if its last three digits are divisible by 8.

120
Q

What is the divisibility rule for 9?

A

A number is divisible by 9 if the sum of its digits is a multiple of 9.

121
Q

What is the rule for divisibility by 10?

A

A number is divisible by 10 if it ends in 0.

122
Q

How can you identify when to use the HCF in a word problem?

A

HCF is used when splitting items into equal groups or finding the greatest common amount.

123
Q

How can you identify when to use the LCM in a word problem?

A

LCM is used when finding when events repeat or aligning cycles to occur simultaneously.

124
Q

Which numbers in the set (23, 65, 92, 10, 104, 70, 500, 21, 64, 798, 1223) are divisible by 5?

A

65, 10, 70, and 500 (ends in 0 or 5).

125
Q

Which numbers in the set are divisible by 8?

A

104, 64, and 500 (last three digits divisible by 8).

126
Q

Which numbers in the set are divisible by 3?

A

21, 798 (sum of digits is a multiple of 3).

127
Q

Is 625 divisible by 5? (True/False)

A

True (ends in 5).

128
Q

Is 88 divisible by 3? (True/False)

A

False (sum of digits = 16, not a multiple of 3).

129
Q

Is 640 divisible by 6? (True/False)

A

False (divisible by 2 but not 3).

130
Q

Is 346 divisible by 4? (True/False)

A

False (last two digits 46, not divisible by 4).

131
Q

Is 476 divisible by 8? (True/False)

A

False (last three digits not divisible by 8).

132
Q

Is 2340 divisible by 9? (True/False)

A

True (sum of digits = 9, divisible by 9).

133
Q

Is 2890 divisible by 6? (True/False)

A

False (divisible by 2 but not 3).

134
Q

Is 4562 divisible by 3? (True/False)

A

False (sum of digits = 17, not divisible by 3).

135
Q

Is 40,090 divisible by 5? (True/False)

A

True (ends in 0).

136
Q

Is 123,456 divisible by 9? (True/False)

A

True (sum of digits = 21, divisible by 9).

137
Q

Can $34.07 be divided equally among 2 people?

A

No (not divisible by 2).

138
Q

Can $34.07 be divided equally among 3 people?

A

No (not divisible by 3).

139
Q

Can $34.07 be divided equally among 9 people?

A

No (not divisible by 9).

140
Q

If a number is divisible by 12, what other numbers must it be divisible by?

A

2, 3, 4, and 6.

141
Q

If a number is divisible by 36, what other numbers must it be divisible by?

A

2, 3, 4, 6, 9, and 12.

142
Q

How do you test if a number is divisible by 12?

A

Check divisibility by both 3 and 4.

143
Q

How do you test if a number is divisible by 15?

A

Check divisibility by both 3 and 5.

144
Q

How do you test if a number is divisible by 24?

A

Check divisibility by both 3 and 8.

145
Q

Jacqueline takes 3 seconds for a full turn, and Sophia takes 4 seconds. How many turns does Jacqueline make when they face each other again?

A

4 turns (LCM of 3 and 4 = 12 seconds; Jacqueline makes 12 ÷ 3 = 4 turns).

Mathematics (6 decks)

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