Prime and Composite Numbers (Grade 4)
A prime number has exactly two factors: 1 and itself (like 7 — only 1 and 7 divide it).
Understanding prime and composite numbers
A composite number has more than two factors (like 12). The number 1 is neither prime nor composite (it has only one factor). To test a number, look for factor pairs: try dividing it by 2, then 3, then 4, and so on. If one of them divides it evenly, the number is composite; if none does, it's prime. You can stop once the number you are trying, times itself, is bigger than the number you are testing, because any factor pair would already have turned up.
Seeing it in action
Worked example
Is 7 prime or composite?
Try 2: 7 ÷ 2 leaves a remainder. Try 3: 3 × 3 = 9 is already bigger than 7, so you can stop. → the only factor pair is 1 × 7. → Prime.
7 squares only make a single row, because 1 × 7 is 7’s only factor pair: 7 is prime. 21 squares also make 3 rows of 7, so 21 is composite.
Worked example 2
Is 21 prime or composite?
3 divides 21 (3×7 = 21). → it has a factor besides 1 and itself. → Composite.
A common mistake, and the fix
Calling every odd number prime, or calling 1 prime.
9, 15 and 21 are odd but composite (21 = 3 × 7), and 2 is the only even prime. 1 has only one factor, itself, so it is neither prime nor composite.
Try a few
Is 13 prime?
Is 15 prime?
3 × 5.
Is 9 prime?
3 × 3.
Factor Fields
A calm number-theory game for factors, multiples, primes, GCF, and LCM.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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