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 31 have?
31 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 39 have?
39 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 56 have?
56 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 38 have?
38 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 11 have?
11 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 24 have?
24 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 50 have?
50 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 17 have?
17 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 6 have?
6 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 49 have?
49 h · Counting positive divisors

12 questions · Seed 48 · 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 31 have?
2
The positive divisors of 31 are 1, 31, which is 2 factors in total.
2. 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.
3. How many positive whole-number factors (divisors) does 56 have?
8
The positive divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, which is 8 factors in total.
4. How many positive whole-number factors (divisors) does 15 have?
4
The positive divisors of 15 are 1, 3, 5, 15, which is 4 factors in total.
5. How many positive whole-number factors (divisors) does 38 have?
4
The positive divisors of 38 are 1, 2, 19, 38, which is 4 factors in total.
6. 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.
7. 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.
8. How many positive whole-number factors (divisors) does 24 have?
8
The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, which is 8 factors in total.
9. How many positive whole-number factors (divisors) does 50 have?
6
The positive divisors of 50 are 1, 2, 5, 10, 25, 50, which is 6 factors in total.
10. How many positive whole-number factors (divisors) does 17 have?
2
The positive divisors of 17 are 1, 17, which is 2 factors in total.
11. How many positive whole-number factors (divisors) does 6 have?
4
The positive divisors of 6 are 1, 2, 3, 6, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 49 have?
3
The positive divisors of 49 are 1, 7, 49, which is 3 factors in total.

12 questions · Seed 48 · 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 31 have?
31 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 39 have?
39 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 56 have?
56 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 38 have?
38 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 11 have?
11 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 24 have?
24 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 50 have?
50 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 17 have?
17 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 6 have?
6 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 49 have?
49 h · Counting positive divisors

12 questions · Seed 48 · 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 31 have?
2
The positive divisors of 31 are 1, 31, which is 2 factors in total.
2. 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.
3. How many positive whole-number factors (divisors) does 56 have?
8
The positive divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, which is 8 factors in total.
4. How many positive whole-number factors (divisors) does 15 have?
4
The positive divisors of 15 are 1, 3, 5, 15, which is 4 factors in total.
5. How many positive whole-number factors (divisors) does 38 have?
4
The positive divisors of 38 are 1, 2, 19, 38, which is 4 factors in total.
6. 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.
7. 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.
8. How many positive whole-number factors (divisors) does 24 have?
8
The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, which is 8 factors in total.
9. How many positive whole-number factors (divisors) does 50 have?
6
The positive divisors of 50 are 1, 2, 5, 10, 25, 50, which is 6 factors in total.
10. How many positive whole-number factors (divisors) does 17 have?
2
The positive divisors of 17 are 1, 17, which is 2 factors in total.
11. How many positive whole-number factors (divisors) does 6 have?
4
The positive divisors of 6 are 1, 2, 3, 6, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 49 have?
3
The positive divisors of 49 are 1, 7, 49, which is 3 factors in total.

12 questions · Seed 48 · Age guidance, not curriculum certification