Free printable prime and composite numbers chart
Grades 4–7Which numbers have exactly two factors and which have more, with all 25 primes below 100 and why 1 belongs to neither group. Print it for the wall, or run the sieve below and find the primes for yourself.
Tap the chart to open it at full size
The numbers 1 to 100
Tap any square to see its factors and whether it is prime or composite. The shaded squares are the 25 primes below 100, and 1 sits on its own because it is neither.
Then switch to sieve mode and find them yourself. Cross out the multiples of 2, then 3, then 5, then 7, and whatever is still standing is prime. This is the Sieve of Eratosthenes, and it is about 2,200 years old.
Four rounds is genuinely enough, which surprises people. Any composite number below 100 must have a factor of 10 or less, so once the multiples of 2, 3, 5 and 7 are gone there is nothing composite left to remove. Worth saying out loud when the sieve finishes, because it looks like a trick until you see why it works.
- Tap a number
- There are 25 primes below 100
- Its factors
- —
Shaded squares are prime. Tap any number to see what divides into it.
How to use this prime and composite chart at home
Build rectangles before defining anything. Give a child twelve counters and ask how many different rectangles they can make: 1 by 12, 2 by 6, 3 by 4. Then give them seven counters. There is only one rectangle, a single row, and that is what prime means — it cannot be arranged any other way.
That model does more than the definition does, because it explains why primes matter rather than just what they are. It also makes 1 obviously odd: one counter makes one rectangle, but so does 7, and yet they behave completely differently.
Then run the sieve above together. Doing the crossing out by hand, in order, is the part that makes the pattern visible — the multiples of 2 disappear in stripes, then the 3s, and by the time the 7s go there is almost nothing left to remove.
Why primes are worth caring about
Every whole number above 1 breaks into primes in exactly one way. 12 is 2 × 2 × 3 and nothing else will do. That uniqueness is the reason primes get called the building blocks of arithmetic, and it is not a figure of speech — it is a theorem.
It is also why they turn up everywhere later. Simplifying fractions is cancelling shared prime factors. Finding a common denominator is combining them. Highest common factor and lowest common multiple are both prime factorization wearing different clothes.
And modern encryption rests on the fact that multiplying two large primes is easy while pulling the product apart again is not. Worth mentioning to a child who asks what this is for, because the honest answer is unusually impressive.
The stopping rule that saves all the work
To test whether a number is prime, you do not have to try every smaller number. You only need to try the primes up to its square root.
The reason is neat: if a number has a factor bigger than its square root, it must also have a matching one below it, because the two multiply to make the number. So if nothing small divides in, nothing large will either.
For 91 that means testing 2, 3, 5 and 7 only — and 7 goes in thirteen times, so 91 is composite. Children who do not know this rule test all the way up to 90 and reasonably conclude that primes are miserable.
Where prime and composite usually go wrong
Thinking prime means odd. It puts 2 in the wrong group and lets 9, 15, 21 and 25 through. Odd and prime overlap heavily and are not the same test.
Calling 1 prime. Understandable, since it is not composite either, and children dislike leftovers. Exactly two factors is the phrase to keep repeating.
Missing 9, 21, 25, 27 and 49. These are the composite numbers that look prime — they are odd, they are not obviously in the 2, 3 or 5 tables, and they get waved through. Every one of them is caught by testing 3 and 7.
Confusing factors with multiples. Factors divide into a number and are smaller or equal; multiples are what you get by multiplying it and are bigger or equal. The words sound related and point in opposite directions.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- factors multiples at Mathify Kids — every topic in this area, sorted by grade.
- prime numbers worksheets — printable practice.
- divisibility rules worksheets — the next step once this is solid.
- factors and multiples worksheets — more practice in the same area.
Everything at this level: Grade 4 math · Grade 5 math · Grade 6 math · Grade 7 math
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Questions parents ask
What is a prime number?
A number with exactly two factors: 1 and itself. 7 is prime because only 1 and 7 divide into it. The word exactly is doing all the work in that definition, and it is what rules 1 out.
What is a composite number?
A number with more than two factors, which means it can be built by multiplying smaller numbers together. 12 is composite because 1, 2, 3, 4, 6 and 12 all divide into it. Every whole number above 1 is either prime or composite, with nothing in between.
Why is 1 not a prime number?
Because it has only one factor — itself — and a prime needs exactly two. It is not an arbitrary exclusion either: if 1 counted as prime, every number could be broken into prime factors in infinitely many ways, since you could keep multiplying by 1. Leaving it out keeps prime factorization unique.
Is 2 a prime number?
Yes, and it is the only even one. Every other even number has 2 as a factor on top of 1 and itself, which gives it at least three factors. Children often assume prime means odd, which then makes 9, 15 and 21 look prime and 2 look wrong.
What are the prime numbers up to 100?
There are 25 of them: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. They thin out as the numbers get bigger, which is a pattern worth noticing on the grid above.
How can you tell if a number is prime?
Try dividing by each prime in turn — 2, 3, 5, 7 and so on — and stop once the divisor squared is bigger than your number. For 91 you need only test 2, 3, 5 and 7, and 7 divides in exactly, so 91 is composite. That stopping rule saves an enormous amount of work.
Is this prime numbers chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.