What Are Prime Numbers? A Grade 6 Guide

A prime number has exactly two factors, 1 and itself, while a composite number has more than two factors. I tell a prime from a composite by listing its factors: if only 1 and the number itself divide it exactly, it is prime. That one check sorts every whole number into its box.

What Is a Prime Number?

A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. The number 7 is prime because only 1 and 7 divide it exactly, while 6 is not prime because 1, 2, 3 and 6 all divide it. Two is the smallest prime number.

I call prime numbers the loners of the number line, because they only ever sit with 1 and themselves. The first primes are 2, 3, 5, 7, 11, 13, 17 and 19, and I ask children to learn them by heart, like a times table in reverse.

A factor is a number that divides another number exactly. I explain factors in full in my Factors and Multiples guide, where listing factors in pairs is the whole game.

What Is a Composite Number?

A composite number is a whole number greater than 1 that has more than two factors. The number 12 is composite because 1, 2, 3, 4, 6 and 12 all divide it, and 27 is composite because 3 and 9 divide it. Every whole number above 1 is either prime or composite.

Most numbers are composite, and that surprises children. Once you pass 10, primes get rarer and rarer, while composite numbers pile up fast. That is why the check matters: you cannot guess, you have to test.

The word “composite” comes from the idea of being made up of parts. A composite number is built from smaller factors, like 12 is built from 2, 3, 4 and 6.

How Do You Check If a Number Is Prime?

To check if a number is prime, try dividing it by 2, 3, 5 and 7, and keep going with larger primes up to half the number. If none divides it, the number is prime. For 29, none of 2, 3, 5, 7, 11 or 13 divide it, so 29 is prime.

Start with 2, because every even number bigger than 2 is composite straight away. Then try 3, 5 and 7, and keep going with the next primes. For Grade 6, you only need to test up to half the number, because any factor bigger than half would pair with 1.

Try it on 17. It is not even, 1 + 7 is 8, so 3 does not divide it, and it does not end in 5 or 0. Half of 17 is 8 and a half, so test 2, 3, 5 and 7 only. None divide it, so 17 is prime.

Breaking numbers into prime factors is also how I find the greatest common factor, and that is the skill Common Core standard 6.NS.B.4 asks for.

Is 1 Prime or Composite?

The number 1 is neither prime nor composite, because it has only one factor: itself. A prime needs exactly two factors, and a composite needs more than two, so 1 fits in neither box. That is why the list of primes starts at 2, not at 1.

This is the mistake I correct most often, and it is an easy one to make. Children see 1 at the start of the number line and assume it must be prime. I tell them 1 is in a box of its own, and once they hear that, they stop putting it in the wrong list.

What Mistakes Do Children Make Most With Prime Numbers?

The biggest mistake is calling 1 a prime number, when 1 is neither prime nor composite. Children also forget that 2 is prime, and they think every odd number is prime, when 9, 15, 21 and 27 are all odd and all composite.

The fix for the odd-number trap is one test: try dividing by 3. Nine, 15, 21 and 27 are all odd, but 3 divides every one of them, so all four are composite. Odd does not mean prime, and even does not mean composite, because 2 is even and prime.

I keep a short list on the board: 1 is neither, 2 is prime, and odd is not a test. Three lines, and the three commonest errors fall away.

A Real-Life Case: Splitting a Class Into Teams

Here is one case, worked in full, the way I do it in class.

Step 1: I have 24 children and I want equal teams with no one left out. Because 24 is composite, it splits into teams of 2, 3, 4, 6, 8 or 12, and I can pick the size that fits the game.

Step 2: Now I have 23 children. Because 23 is prime, it only splits into 1 team of 23 or 23 teams of 1, and neither is a team game. I have to change the plan, or ask one more child to join.

Step 3: The rule is simple: composite numbers give you choices, prime numbers give you none. That is why a teacher checks the number before the lesson, not during it.

Try It Yourself: 3 Practice Questions

Cover the answers, try all three, then check.

1. Is 17 a prime number?
2. Is 27 a prime number?
3. List the prime numbers under 20.

Answers

1. Yes, 17 is prime. Only 1 and 17 divide it exactly.
2. No, 27 is not prime. It is composite, because 27 = 3 × 9.
3. 2, 3, 5, 7, 11, 13, 17, 19. These are the only primes under 20.

Key Takeaways

• Prime: exactly two factors, 1 and itself.
• Composite: more than two factors.
• 1 is neither: it has only one factor.
• Check by dividing: try 2, 3, 5, 7 and on, up to half the number.
• Odd is not a test: 9, 15, 21 and 27 are odd and composite.

If your child answered all three questions, she is ready for a longer page. For more free practice at this level, browse our Grade 6 math worksheets page. Every sheet is free to print.