3.1 Factors, multiples and divisibility — Practise

1. Write down all the factors of 24.

Answer: $1, 2, 3, 4, 6, 8, 12$ and $24$. The factors pair up — $1\times24$, $2\times12$, $3\times8$, $4\times6$ — which is why you can stop at the square root.

2. How many factors does 36 have?

Answer: Nine: $1, 2, 3, 4, 6, 9, 12, 18$ and $36$. Because $36=6^2$, the factor $6$ pairs with itself, so there is an odd number of them.

3. Write down the first four multiples of 7.

Answer: $7, 14, 21$ and $28$. A multiple of 7 is $7$ times a whole number.

4. Is 1234 divisible by 3?

Answer: No. The digit sum is $1+2+3+4=10$, and 10 is not a multiple of 3. A number is divisible by 3 when its digit sum is, and 1234 is not.

5. Is 4512 divisible by 6?

Answer: Yes. It is even, so it divides by 2. Its digit sum is $4+5+1+2=12$, which is a multiple of 3, so it divides by 3. Dividing by 2 and by 3 means it divides by 6.

6. List the square numbers between 40 and 100.

Answer: $49$, $64$ and $81$. These are $7^2$, $8^2$ and $9^2$; $6^2=36$ is too small and $10^2=100$ is not between.

7. Work out $4^3$.

Answer: $4^3=4\times4\times4=64$, so 64 is a cube number.