ReasoningAges 13-15

Counting positive divisors

Use the prime factorisation exponents (a + 1)(b + 1) to count all positive divisors of a number. Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 13-15

Counting positive divisors

Take your time. Show your thinking.

1. How many positive whole-number factors (divisors) does 36 have?
36 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 29 have?
29 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 48 have?
48 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 32 have?
32 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 8 have?
8 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 25 have?
25 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 22 have?
22 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 9 have?
9 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 18 have?
18 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 34 have?
34 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 45 have?
45 h · Counting positive divisors

12 questions · Seed 104732 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Counting positive divisors

Answers and reasoning. Review before teaching.

1. How many positive whole-number factors (divisors) does 36 have?
9
The positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36, which is 9 factors in total.
2. How many positive whole-number factors (divisors) does 29 have?
2
The positive divisors of 29 are 1, 29, which is 2 factors in total.
3. How many positive whole-number factors (divisors) does 48 have?
10
The positive divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, which is 10 factors in total.
4. How many positive whole-number factors (divisors) does 32 have?
6
The positive divisors of 32 are 1, 2, 4, 8, 16, 32, which is 6 factors in total.
5. How many positive whole-number factors (divisors) does 8 have?
4
The positive divisors of 8 are 1, 2, 4, 8, which is 4 factors in total.
6. How many positive whole-number factors (divisors) does 25 have?
3
The positive divisors of 25 are 1, 5, 25, which is 3 factors in total.
7. How many positive whole-number factors (divisors) does 22 have?
4
The positive divisors of 22 are 1, 2, 11, 22, which is 4 factors in total.
8. How many positive whole-number factors (divisors) does 9 have?
3
The positive divisors of 9 are 1, 3, 9, which is 3 factors in total.
9. How many positive whole-number factors (divisors) does 28 have?
6
The positive divisors of 28 are 1, 2, 4, 7, 14, 28, which is 6 factors in total.
10. How many positive whole-number factors (divisors) does 18 have?
6
The positive divisors of 18 are 1, 2, 3, 6, 9, 18, which is 6 factors in total.
11. How many positive whole-number factors (divisors) does 34 have?
4
The positive divisors of 34 are 1, 2, 17, 34, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 45 have?
6
The positive divisors of 45 are 1, 3, 5, 9, 15, 45, which is 6 factors in total.

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Counting positive divisors

Take your time. Show your thinking.

1. How many positive whole-number factors (divisors) does 36 have?
36 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 29 have?
29 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 48 have?
48 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 32 have?
32 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 8 have?
8 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 25 have?
25 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 22 have?
22 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 9 have?
9 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 18 have?
18 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 34 have?
34 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 45 have?
45 h · Counting positive divisors

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Counting positive divisors

Answers and reasoning. Review before teaching.

1. How many positive whole-number factors (divisors) does 36 have?
9
The positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36, which is 9 factors in total.
2. How many positive whole-number factors (divisors) does 29 have?
2
The positive divisors of 29 are 1, 29, which is 2 factors in total.
3. How many positive whole-number factors (divisors) does 48 have?
10
The positive divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, which is 10 factors in total.
4. How many positive whole-number factors (divisors) does 32 have?
6
The positive divisors of 32 are 1, 2, 4, 8, 16, 32, which is 6 factors in total.
5. How many positive whole-number factors (divisors) does 8 have?
4
The positive divisors of 8 are 1, 2, 4, 8, which is 4 factors in total.
6. How many positive whole-number factors (divisors) does 25 have?
3
The positive divisors of 25 are 1, 5, 25, which is 3 factors in total.
7. How many positive whole-number factors (divisors) does 22 have?
4
The positive divisors of 22 are 1, 2, 11, 22, which is 4 factors in total.
8. How many positive whole-number factors (divisors) does 9 have?
3
The positive divisors of 9 are 1, 3, 9, which is 3 factors in total.
9. How many positive whole-number factors (divisors) does 28 have?
6
The positive divisors of 28 are 1, 2, 4, 7, 14, 28, which is 6 factors in total.
10. How many positive whole-number factors (divisors) does 18 have?
6
The positive divisors of 18 are 1, 2, 3, 6, 9, 18, which is 6 factors in total.
11. How many positive whole-number factors (divisors) does 34 have?
4
The positive divisors of 34 are 1, 2, 17, 34, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 45 have?
6
The positive divisors of 45 are 1, 3, 5, 9, 15, 45, which is 6 factors in total.

12 questions · Seed 104732 · Age guidance, not curriculum certification