Prime and Composite Numbers, Class 5: A Ten-Minute Lesson and a Quiz

Ask a Class 5 child what a prime number is and you will often hear "a number that can only be divided by one and itself". It is nearly right, and the gap between nearly right and right is exactly where the marks go.

The one sentence that is the whole topic

A prime number has exactly two factors: 1 and itself. A composite number has more than two. That is all of it.

Notice what the sentence does that the usual version does not. It counts factors instead of describing division. Counting factors settles every awkward case at once:

• 1 has one factor (itself). Not two. So it is neither prime nor composite.
• 2 has two factors (1 and 2). Prime, and the only even one.
• 9 has three factors (1, 3, 9). Composite, even though it is odd, which surprises a lot of children who have quietly decided that odd means prime.

A quick test for any number under 100

Try dividing by 2, 3, 5 and 7. If none of them go in exactly, the number is prime. That works for everything below 100 because the next prime, 11, squared is 121.

Take 91. It is odd, so not 2. Its digits add up to 10, so not 3. It does not end in 0 or 5, so not 5. Now 7: 7 × 13 is 91. Composite. Most children guess 91 is prime; the test says otherwise in four steps.

Why it matters more than it looks

Primes are the atoms of arithmetic. Every whole number above 1 is either prime or a product of primes, and that product is unique. Class 6 uses exactly this to find the highest common factor and lowest common multiple: write each number as a product of primes and read the answer off. A child who learned primes as "odd numbers, mostly" cannot do that. A child who learned to count factors can.

Where to practise

The Class 5 lesson Prime and Composite Numbers is free to read without an account. It walks through the definition, the test and the common traps one screen at a time, then ends on a quiz about the same topic. The Class 6 follow-on, Primes, HCF and LCM, is also free and picks up where the first one stops.

The quizzes come at three levels. Start with the easy one: it takes about ten minutes, marks itself, and shows every correct answer with the reason at the end. Fifty per cent or better earns credits that open the maths games.