HCF — highest common factor

A factor of a number divides into it exactly, leaving no remainder. We need to check which option divides into 30 exactly.

Check: $30÷8=3.75$ (remainder), $30÷9=\mathrm{3.33...}$ (remainder), $30÷13=\mathrm{2.3...}$ (remainder), $30÷15=2$ exactly.

Since $15\times 2=30$, the number 15 divides exactly into 30 with no remainder. So 15 is a factor of 30.

We need the option that divides exactly into 30. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.

$30÷8=3$ remainder $6$. 8 is not a factor of 30, so eliminate this option.

$30÷9=3$ remainder $3$, and $30÷13=2$ remainder $4$. Neither 9 nor 13 divides exactly into 30.

$30÷15=2$ exactly. 15 is a factor of 30 and is the correct answer.

To find all factors of 12, list every factor pair: $1\times 12=12$, $2\times 6=12$, $3\times 4=12$.

From the pairs, the individual factors of 12 are: 1, 2, 3, 4, 6, 12.

Counting the list: 1, 2, 3, 4, 6, 12 — that is 6 factors in total.

The factors of 12 are: 1, 2, 3, 4, 6, 12. We now check each answer option against this list.

4 factors would mean only four numbers divide into 12, but we already found more than four. Eliminate 4.

There are not 5 or 7 numbers in the factor list — the complete list has exactly six entries. Eliminate 5 and 7.

The factor list 1, 2, 3, 4, 6, 12 contains 6 numbers, so the answer is 6.