Prime Factors, HCF & LCM Practice Questions

Write $198$ as a product of its prime factors.

Write down the number in the list that is a prime number.

Write down the three numbers in the list that are multiples of $7$.

Write down all the factors of $45$.

Write down the highest common factor (HCF) of $A$ and $B$.

Find the lowest common multiple (LCM) of $A$ and $B$.

Amina is making party bags.

Candles are sold in packs of $15$.
Candle holders are sold in packs of $18$.

Amina wants to buy exactly the same number of candles as candle holders.

Work out the smallest number of packs of candles and the smallest number of packs of candle holders she can buy.

Work out the side length of the largest square tile he can use.

Using tiles of this size, work out the number of tiles Joe needs.

Write $540$ as a product of its prime factors. Give your answer in index form.

$540 \times n$ is a square number, where $n$ is a positive integer.

Find the smallest possible value of $n$.

$n$ is a positive integer.

The highest common factor (HCF) of $24$ and $n$ is $8$.
The lowest common multiple (LCM) of $24$ and $n$ is $120$.

Find the value of $n$.

Explain how you can tell from this that $A$ is not a square number.

Find the smallest positive integer $k$ such that $A \times k$ is a square number.

Find the smallest positive integer $m$ such that $A \times m$ is a cube number.

Find the value of $p$.

Find the highest common factor (HCF) of $x$ and $y$.