ReasoningAges 10-12

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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 10-12

Counting positive divisors

Take your time. Show your thinking.

1. How many positive whole-number factors (divisors) does 58 have?
58 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 11 have?
11 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 23 have?
23 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 47 have?
47 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 36 have?
36 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 32 have?
32 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 39 have?
39 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 16 have?
16 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 59 have?
59 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 8 have?
8 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 57 have?
57 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 52 have?
52 h · Counting positive divisors

12 questions · Seed 104730 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Counting positive divisors

Answers and reasoning. Review before teaching.

1. How many positive whole-number factors (divisors) does 58 have?
4
The positive divisors of 58 are 1, 2, 29, 58, which is 4 factors in total.
2. How many positive whole-number factors (divisors) does 11 have?
2
The positive divisors of 11 are 1, 11, which is 2 factors in total.
3. How many positive whole-number factors (divisors) does 23 have?
2
The positive divisors of 23 are 1, 23, which is 2 factors in total.
4. How many positive whole-number factors (divisors) does 47 have?
2
The positive divisors of 47 are 1, 47, which is 2 factors in total.
5. 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.
6. 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.
7. How many positive whole-number factors (divisors) does 39 have?
4
The positive divisors of 39 are 1, 3, 13, 39, which is 4 factors in total.
8. How many positive whole-number factors (divisors) does 16 have?
5
The positive divisors of 16 are 1, 2, 4, 8, 16, which is 5 factors in total.
9. How many positive whole-number factors (divisors) does 59 have?
2
The positive divisors of 59 are 1, 59, which is 2 factors in total.
10. 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.
11. How many positive whole-number factors (divisors) does 57 have?
4
The positive divisors of 57 are 1, 3, 19, 57, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 52 have?
6
The positive divisors of 52 are 1, 2, 4, 13, 26, 52, which is 6 factors in total.

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Counting positive divisors

Take your time. Show your thinking.

1. How many positive whole-number factors (divisors) does 58 have?
58 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 11 have?
11 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 23 have?
23 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 47 have?
47 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 36 have?
36 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 32 have?
32 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 39 have?
39 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 16 have?
16 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 59 have?
59 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 8 have?
8 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 57 have?
57 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 52 have?
52 h · Counting positive divisors

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Counting positive divisors

Answers and reasoning. Review before teaching.

1. How many positive whole-number factors (divisors) does 58 have?
4
The positive divisors of 58 are 1, 2, 29, 58, which is 4 factors in total.
2. How many positive whole-number factors (divisors) does 11 have?
2
The positive divisors of 11 are 1, 11, which is 2 factors in total.
3. How many positive whole-number factors (divisors) does 23 have?
2
The positive divisors of 23 are 1, 23, which is 2 factors in total.
4. How many positive whole-number factors (divisors) does 47 have?
2
The positive divisors of 47 are 1, 47, which is 2 factors in total.
5. 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.
6. 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.
7. How many positive whole-number factors (divisors) does 39 have?
4
The positive divisors of 39 are 1, 3, 13, 39, which is 4 factors in total.
8. How many positive whole-number factors (divisors) does 16 have?
5
The positive divisors of 16 are 1, 2, 4, 8, 16, which is 5 factors in total.
9. How many positive whole-number factors (divisors) does 59 have?
2
The positive divisors of 59 are 1, 59, which is 2 factors in total.
10. 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.
11. How many positive whole-number factors (divisors) does 57 have?
4
The positive divisors of 57 are 1, 3, 19, 57, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 52 have?
6
The positive divisors of 52 are 1, 2, 4, 13, 26, 52, which is 6 factors in total.

12 questions · Seed 104730 · Age guidance, not curriculum certification