Prime and composite numbers, shown with rectangles

For: Ages 8-11. Updated 2026-10-15.

Take 12 blocks. You can lay them out as 2 rows of 6, 3 rows of 4, or one long line of 12. Now take 7 blocks. However you try, the only rectangle is one line of 7. Numbers like 12 that make a proper rectangle are composite. Numbers like 7 that only make a line are prime.

The definition

A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. The number 1 has only one factor, so it is neither prime nor composite, and neither is 0.

2 is the only even prime. Every other even number can be split into 2 rows, so it is composite.

Testing a number by hand

1. If it is even and bigger than 2, it is composite.
2. Add the digits. If the total is a multiple of 3, the number is a multiple of 3.
3. If it ends in 0 or 5 and is bigger than 5, it is a multiple of 5.
4. Try dividing by 7, 11, 13 and so on. You only need to try primes up to the square root. For 91 that means primes up to 9, and 91 = 7 × 13, so it is composite.

The 25 primes below 100

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Numbers that often fool people: 51 (3 × 17), 57 (3 × 19), 87 (3 × 29) and 91 (7 × 13). They look prime, but all of them are composite.

Check 91 in the Number Blocks Tool to see its rectangles. Open the tool with 91

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