Special Numbers

Question 1

Divisibility Rule for 2

Answer 1

Any even integer - a number whose last digit is 0, 2, 4, 6 or 8.

Question 2

Divisibility Rule for 3

Answer 2

Any integer where the sum of the digits is a multiple of 3.

Question 3

Divisibility Rule for 4

Answer 3

Any even integer whose last two digits are divisible by 4.

Question 4

Divisibility Rule for 5

Answer 4

Any integer whose last digits is a 0 or a 5.

Question 5

Divisibility Rule for 6

Answer 5

Any even integer which is divisible by 3 and 2.

Question 6

Divisibility Rule for 8

Answer 6

Any even integer whose last 3 digits are divisible by 8.

(halve the last 3 digits three times - did you get a whole number?)

Question 7

Divisibility Rule for 9

Answer 7

Any integer where the sum of digits is divisible by 9.

Question 8

Divisibility Rule for 10

Answer 8

Any integer whose last digit is 0.

Question 9

How do you check for divisibility for larger numbers?

Answer 9

By splitting them into coprime factors
e.g. to test for divisibility by 12 test for divisibility by 3 and 4.

Question 10

Is 1 a prime number?

Answer 10

NO!!!

Question 11

definition of a prime number

Answer 11

a whole number greater than 1 that cannot be exactly divided by any whole number other than itself and 1

Question 12

definition of a factor

Answer 12

a number that divides another number evenly, with no remainder

Question 13

definition of a multiple

Answer 13

the numbers you get when you multiply a certain number by an integer

Question 14

How do you list all the factors of a number systematically?

Answer 14

By dividing the number by each counting number, starting with 1

Question 15

How do you write a number as a product of its prime factors using a factor tree?

Answer 15

1. Write the number at the top of the factor tree.
2. Draw two branches from the number to split the number into a pair of factors, greater than 1.
3. Write each factor at the end of each branch.
4. This process continues until the branches all end in prime numbers.

Question 16

How do you find the highest common factor (HCF) of 2 numbers?

Answer 16

The highest common factor is found by multiplying all the factors which appear in both lists

Question 17

How do you find the lowest common multiple (LCM) of 2 numbers?

Answer 17

List out all multiples of both numbers and highlight the LCM

Question 18

How do you use a Venn Diagram to find the HCF & LCM of 2 numbers?

Answer 18

1. Break the numbers into the product of prime factors using prime factor trees, as before.
2. Put each prime factor in the correct place in the Venn diagram. Any common factors should be placed in the intersection of the two circles.

The highest common factor (HCF) is found by multiplying together the numbers in the intersection of the two circles.

The lowest common multiple (LCM) is found by multiplying together the numbers from all three sections of the circles.

Question 19

definition of an integer

Answer 19

a number that is not a fraction; a whole number.

Question 20

definition of a perfect number

Answer 20

a positive integer that is equal to the sum of its proper divisors.

Question 21

definition of a square number

Answer 21

the product of a number multiplied by itself

Question 22

definition of a cube number

Answer 22

a number that has been multiplied by itself and then multiplied by itself again.

Question 23

definition of a triangular number

Answer 23

a number that can be represented by a pattern of dots arranged in an equilateral triangle with the same number of dots on each side.

Question 24

How do you multiple and divide decimals?

Answer 24

Remove the decimal place, complete the calculation, put the decimal place back.