Factors, Multiples and Primes Help: Why Your Child Keeps Getting Stuck (And What Actually Works)

Ask your child what a factor is and they will tell you. Ask them for the highest common factor of 24 and 36 and you get a pause, then a guess.

I'm Aadam, and I've taught this topic to hundreds of 11+ and GCSE students at SHLC. The definitions are rarely the problem. What goes missing is a reliable way to find the answer once the numbers get too big to see.

The real problem isn't the definitions

Two things go wrong, and both look like carelessness. Both are method gaps.

Factors and multiples get swapped. The two words sound alike, they are taught in the same lesson, and a child under time pressure reaches for whichever one comes to mind. Factors go into a number and are smaller than it. Multiples come out of a number and are bigger than it. A child who can say that sentence stops swapping them.

Factors get hunted at random. Asked for the factors of 36, most children start writing 1, 2, 3, 4, 6, 9 and then stall, unsure whether they have them all. They are guessing which numbers divide in, one at a time, with nothing telling them when to stop.

The fix for the second one takes a minute to teach. Work in pairs, upwards from 1, and stop when the pairs meet in the middle. Once your child does that, they know they have every factor, because the pairs meeting in the middle is the proof.

Why worksheets alone don't fix it

A worksheet on this topic asks for the factors of twenty different numbers. A child who hunts at random gets most of them nearly right, misses one factor each time, and never finds out that the hunting is the problem.

The hardest questions here never use the words either. An 11+ paper does not ask for the lowest common multiple of 12 and 18. It asks when two buses leaving every 12 and 18 minutes will next leave together. Your child has to work out which tool the question wants, and a worksheet headed Lowest Common Multiple has already done that for them.

The factors, multiples and primes skills that trip children up, in order

Skip the pair method at the start and HCF questions stay guesswork for years, so this order matters.

1. Saying what a factor and a multiple are in a sentence. Not reciting the definition, but explaining it about a specific number, out loud.

2. Listing every factor in pairs. Working up from 1, writing each pair as you find it, stopping when the two sides meet. The rest of the topic sits on this one.

3. Divisibility tests. Knowing quickly whether a number divides by 2, 3, 4, 5, 6, 9 and 10, so the pair hunt takes seconds rather than minutes.

4. What makes a number prime. Exactly two factors, itself and 1, which is why 1 is not prime and 2 is the only even prime.

5. Prime factorisation and index form. Breaking a number down until only primes are left, then writing it with powers.

6. HCF and LCM by listing. Works for small numbers and is worth doing first, because it shows the child what the answer means.

7. HCF and LCM from prime factors. The method that still works when the numbers are too big to list, using a Venn diagram to hold the shared factors.

8. Worded problems that name neither. Buses leaving together, cutting ribbon into equal pieces, making identical party bags. Most of the marks in this topic sit here.

What actually closes the gap

Start with the first of these three. The other two get easier once it is in place.

Teach the pair method and insist on it. Factors written as pairs, working up from 1, stopping when they meet. Your child will find every factor of 36 in under a minute, and will know that none is missing.

Treat prime factors as the fingerprint of a number. Every number breaks down into one unique set of primes. Once a child sees that, HCF is the primes two numbers share and LCM is everything across both, which is one idea instead of two rules.

Practise deciding which tool the question wants. Sit with the worded questions and ask only one thing: is this asking for a number that goes into both, or a number they both go into? Answering that question is a separate skill from the arithmetic, and it is the one the exam tests.

The lessons we built to fix this

Our Factors, Multiples and Primes Bundle follows that order. Three interactive lessons, 13 units, 234 questions.

Factors and Multiples builds the pair method, the divisibility tests and the language, then uses them on worded questions.

HCF and LCM starts by listing so the answer means something, then moves to the prime factor method and the buses and ribbon problems.

Primes and Prime Factorisation covers what makes a number prime, factor trees, index form, and using prime factors to find HCF and LCM.

A worked example runs first in every lesson, revealed a line at a time so your child watches the pairs being built rather than reading a finished list. Nothing is marked for them: they answer, then click to see whether they were right. Three tiers of questions let a child work up instead of drowning at the top.

These three lessons also sit inside The Complete 11+ Maths Course, which numbers all 80 lessons 1 to 80 so you always know what comes next.

What to do this week

Two questions will show you where your child is.

Ask your child to write down every factor of 36. Watch how they do it, not what they write. If they are trying numbers at random rather than working in pairs from 1, teach the pair method first.

Then ask them this: one bus leaves every 12 minutes and another leaves every 18 minutes. They have just left together. When do they next leave together? If they cannot decide whether to look for a common factor or a common multiple, that is the skill to work on first.

Our free factors and multiples practice page has more questions you can use tonight at no cost, and each one names the lesson it comes from, so you can see where the work is needed.

For the whole sequence taught in order, the Factors, Multiples and Primes Bundle covers it end to end, and you can buy the single lesson your child is stuck on instead. If you would rather work out the starting point together, book a free consultation.

Aadam, SHLC Tutors