Factors worksheet for identifying prime and composite numbers and finding factors of numbers from 21 to 40.

Let’s go step by step to solve each part of the worksheet.

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1) Circle the numbers below which are prime numbers:

Numbers given:
25, 17, 24, 13, 9, 11

Prime numbers have exactly two factors: 1 and themselves.

- 25 → factors: 1, 5, 25 → not prime (more than 2 factors)
- 17 → factors: 1, 17 → prime
- 24 → many factors (1,2,3,4,6,8,12,24) → not prime
- 13 → factors: 1, 13 → prime
- 9 → factors: 1, 3, 9 → not prime
- 11 → factors: 1, 11 → prime

✔ Prime numbers: 17, 13, 11

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2) Circle the numbers below which are composite:

Numbers given:
19, 22, 15, 11, 21, 31

Composite numbers have more than 2 factors.

- 19 → only 1 and 19 → prime, not composite
- 22 → 1, 2, 11, 22 → composite
- 15 → 1, 3, 5, 15 → composite
- 11 → only 1 and 11 → prime, not composite
- 21 → 1, 3, 7, 21 → composite
- 31 → only 1 and 31 → prime, not composite

✔ Composite numbers: 22, 15, 21

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3) Find the factors of numbers from 21 to 40.

We’ll list all factors for each number. Remember: a factor is a whole number that divides evenly into the number.

Let’s do them one by one:

Left column:

- 21 → 1, 3, 7, 21 *(already done)*
- 22 → 1, 2, 11, 22
- 23 → 1, 23 *(only two → prime)*
- 24 → 1, 2, 3, 4, 6, 8, 12, 24
- 25 → 1, 5, 25
- 26 → 1, 2, 13, 26
- 27 → 1, 3, 9, 27
- 28 → 1, 2, 4, 7, 14, 28
- 29 → 1, 29 *(prime)*
- 30 → 1, 2, 3, 5, 6, 10, 15, 30

Right column:

- 31 → 1, 31 *(prime)*
- 32 → 1, 2, 4, 8, 16, 32
- 33 → 1, 3, 11, 33
- 34 → 1, 2, 17, 34
- 35 → 1, 5, 7, 35
- 36 → 1, 2, 3, 4, 6, 9, 12, 18, 36
- 37 → 1, 37 *(prime)*
- 38 → 1, 2, 19, 38
- 39 → 1, 3, 13, 39
- 40 → 1, 2, 4, 5, 8, 10, 20, 40

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4) Highlight all the prime numbers in the table above.

From our list above, the primes between 21 and 40 are:

→ 23, 29, 31, 37

(These are the only ones with exactly two factors.)

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5) Which number between 21 and 40 has the most factors?

Let’s count how many factors each number has:

- 21 → 4 factors
- 22 → 4
- 23 → 2
- 24 → 8 factors ← high!
- 25 → 3
- 26 → 4
- 27 → 4
- 28 → 6
- 29 → 2
- 30 → 8 factors ← also high!
- 31 → 2
- 32 → 6
- 33 → 4
- 34 → 4
- 35 → 4
- 36 → 9 factors ← highest so far!
- 37 → 2
- 38 → 4
- 39 → 4
- 40 → 8

Wait — let’s double-check 36:

Factors of 36:
1 × 36
2 × 18
3 × 12
4 × 9
6 × 6 → stop here (don’t repeat)

So: 1, 2, 3, 4, 6, 9, 12, 18, 36 → that’s 9 factors

Now check 24: 1,2,3,4,6,8,12,24 → 8 factors
30: 1,2,3,5,6,10,15,30 → 8 factors
40: 1,2,4,5,8,10,20,40 → 8 factors

Yes — 36 has 9 factors, which is more than any other number between 21 and 40.

✔ So the answer is 36

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Final Answer:
1) Prime numbers: 17, 13, 11
2) Composite numbers: 22, 15, 21
3) Factors listed above for each number from 21 to 40
4) Prime numbers in table: 23, 29, 31, 37
5) Number with most factors: 36