Integer Properties

Question 1

What is the outcome when :

Even x Even
Odd x Odd
Odd x Even

Even + Odd
Even + Even
Odd + Odd

Answer 1

Even x Even = Even
Odd x Odd = Odd
Odd x even = Even

Even + Odd = Odd
Even + Even = Even
Odd + Odd = Even

Question 2

1. What is a factor and a multiple
2. Give 3 multiples of 7 greater than 2401.
3. Give 3 factors of 6

Answer 2

1. Factor is a something that divides evenly into a number and cannot be greater than that number (can be equal to it) . Multiple is something that’s a product of a specific number when multiples by a integer and it cannot be less than that number, must be greater than or equal to it
2. 2408, 2395, 2422. Add or minus 7 from 2401 to get the multiples
3. 2,3 and 6 are factors of 6

Question 3

How would you know if a number is divisible by 2, 3, 4, 5, 6, 8, and 9

Answer 3

Question 4

Prime factorise 48 and find it’s total positive factors

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Pick one answer from 3, 7, 9, 17, 70

Pick one answer from : 3, 7, 16, 19, 70

Answer 7

Answer = 7 (16-(-19) = 35, which is a another multiple of K and is divisible by 7, so 7 is the answer.

Question 8

1. How many different prime factors does 126 have?
2. How many prime factors are there in prime factorisation of 400 including repeats?

Answer 8

1. 3 different prime factors which are 2,3 and 7 ( question is asking for prime factors not factors)
2. 400 = 2^4 x 5^2 = 4+2 = 6

Question 9

What must a remainder be?

Answer 9

It must be less than the divisor.

Question 10

Find the total number of odd factors, and even factors for 21,600

Answer 10

Total Factors - 72

Total odd factors - 12

Total even factors - 60 ( 72 - 12)

Step 1. Prime factorise

Step 2. To find odd factors, add 1 to the exponents of odd factors and then multiply them

Step 3. To find even factors, do total factors - odd factors

Question 11

Answer 11

Question 12

Answer 12

Question 13

What is GCF and LCM

Answer 13

GCF is the greatest possible factor between two numbers, always less than or equal to the original two numbers and

LCM is the lowest common multiple between two number, it has to be equal to or greater than the original two numbers.

Question 14

1. Find GCF of 720 and 1200, show method
2. Find LCM of 24 and 32, using both known methods (normal + formula)

Answer 14

1. GCF = 240, prime factorise, and then look at which common factors along with their exponents is in both numbers. For this example it was - 2^4* 3*5 2.

LCM = 96, prime factorise and find GCF then multiply GCF (8) by certain numbers to get both of the original numbers so 8x3 and 8x4. Now multiply the GCF with 3 and 4 to get the LCM.

LCM formula = A x B/ GCF

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

How can you express consecutive even or odd integers

Answer 18

Question 19

What does Ascending and Descending mean

Answer 19

Ascending means increasing and descending means decreasing

Question 20

Answer 20

Question 21

If N is a positive integer with odd number of factors, which of the following must be true about N : • N must be odd • N must be even • N must be Prime • N must be square • N must be 1

Answer 21

Must be square because if you find the exponents of N and find it’s positive factors then you would find that it has odd factors and only square numbers have odd factors.

Question 22

Suppose M and N are positive integers, and that the greatest common factor/divisor of m and n is 24, while the LCM of M and N is 144. If it can be determined, what is the product of M and N

Answer 22

3456 - product of M and N Use formula of: LCM = Product of M and N/ GCF 144 = Product/24, multiply 24 x 144 to get product

Question 23

Answer 23

Question 24

Can you have a negative number in an square root

Answer 24

No. You can never.