Exactly two factors: prime numbers
The Short Answer
A prime number has exactly two factors: itself and one. That precise definition settles both of the arguments children have. One is not prime, because its only factor is one — that is one factor, not two. Two is prime, because its factors are one and two, and it is the only even prime there is.
The definition, precisely
A prime number has exactly two factors — itself and one.
Not one factor. Not three. Exactly two.
The precision is the point, because a woolly definition is exactly what the examiner is testing.
What that settles
One is not prime. Its only factor is one. That is one factor, not two.
Two is prime. Its factors are one and two — exactly two of them.
And two is the only even prime there is, because every other even number has 2 as an extra factor, which gives it at least three.
Both of those are the arguments children have about primes, and both are settled by the definition rather than by a rule that has to be remembered separately.
The list to know
The primes up to thirty:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Ten of them. Learn that list — it comes up in almost every paper, and knowing it turns a thirty-second question into a three-second one.
Beyond thirty it is better to test than to memorise, because the list grows faster than it is worth learning.
Testing a number
Where do pupils lose marks?
Calling 1 prime, which the exact definition prevents.
Excluding 2 because it is even, having learnt "primes are odd" as a shortcut.
Accepting 51 or 57 without testing.
Confusing prime with odd, which they overlap with and are not.
Try it yourself
Use the definition — exactly two factors — rather than a remembered list, and then check against the list.
- Is 1 a prime number?
- Is 2 a prime number?
- List the primes up to 30.
- Why is 2 the only even prime?
- Is 51 prime?
- No. Its only factor is 1, which is one factor rather than two. The definition settles it without any argument.
- Yes. Its factors are 1 and 2 — exactly two — so it meets the definition precisely.
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Ten of them, and this list is worth knowing by heart.
- Because every other even number has 2 as a factor as well as itself and one, which gives it at least three factors. Only 2 itself escapes that, since its two factors are 1 and 2.
- No. 51 is 3 × 17, so it has four factors. It is a common trap because it looks prime — it is odd and it is not in any times table children recite. Testing by 3 catches it: 5 + 1 = 6, which divides by 3, so 51 does.
How much practice does this type need at home?
Ten numbers to learn, and one habit: when a number comes up in conversation, ask whether it is prime. House numbers, bus numbers, shirt numbers.
The value is not the answer — it is that your child reaches for the definition rather than for a feeling, and after a fortnight the list up to thirty is simply known.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why is 1 not prime?
Because a prime has exactly two factors and 1 has only one — itself. Children argue about this because 1 feels like it ought to qualify, and the examiner is testing precisely whether the definition is woolly or exact. Not one factor. Not three. Exactly two. Once that is the definition, there is nothing to argue about.
How does my child check whether a number is prime?
Try dividing by the small primes in turn — 2, 3, 5, 7, 11 — and stop when the divisor squared passes the number. For 51: not even, so not 2; digits add to 6 which divides by 3, so 51 divides by 3, and it is not prime. Most 11+ numbers are settled by 2, 3 and 5 alone.
Which numbers catch children out?
The ones that look prime and are not. 51 is 3 × 17. 57 is 3 × 19. 91 is 7 × 13. All three are odd, none is in a times table children recite, and all three feel prime. The digit-sum test for 3 catches the first two in a second, and 91 is worth simply knowing.
Is the list up to 30 worth learning?
Yes, and it is the best value in this topic. Ten numbers, and knowing them turns a thirty-second question into a three-second one. Beyond thirty it is better to test than to memorise, since the list grows faster than it is worth learning.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
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