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.

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 13-15

Counting positive divisors

Take your time. Show your thinking.

1. How many positive whole-number factors (divisors) does 47 have?
47 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 46 have?
46 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 24 have?
24 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 51 have?
51 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 48 have?
48 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 43 have?
43 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 57 have?
57 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 53 have?
53 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 56 have?
56 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 9 have?
9 h · Counting positive divisors

12 questions · Seed 49 · 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 47 have?
2
The positive divisors of 47 are 1, 47, which is 2 factors in total.
2. How many positive whole-number factors (divisors) does 46 have?
4
The positive divisors of 46 are 1, 2, 23, 46, which is 4 factors in total.
3. 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.
4. How many positive whole-number factors (divisors) does 51 have?
4
The positive divisors of 51 are 1, 3, 17, 51, which is 4 factors in total.
5. 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.
6. How many positive whole-number factors (divisors) does 43 have?
2
The positive divisors of 43 are 1, 43, which is 2 factors in total.
7. How many positive whole-number factors (divisors) does 54 have?
8
The positive divisors of 54 are 1, 2, 3, 6, 9, 18, 27, 54, which is 8 factors in total.
8. 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.
9. How many positive whole-number factors (divisors) does 53 have?
2
The positive divisors of 53 are 1, 53, which is 2 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 56 have?
8
The positive divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, which is 8 factors in total.
12. 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.

12 questions · Seed 49 · 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 47 have?
47 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 46 have?
46 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 24 have?
24 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 51 have?
51 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 48 have?
48 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 43 have?
43 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 57 have?
57 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 53 have?
53 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 56 have?
56 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 9 have?
9 h · Counting positive divisors

12 questions · Seed 49 · 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 47 have?
2
The positive divisors of 47 are 1, 47, which is 2 factors in total.
2. How many positive whole-number factors (divisors) does 46 have?
4
The positive divisors of 46 are 1, 2, 23, 46, which is 4 factors in total.
3. 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.
4. How many positive whole-number factors (divisors) does 51 have?
4
The positive divisors of 51 are 1, 3, 17, 51, which is 4 factors in total.
5. 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.
6. How many positive whole-number factors (divisors) does 43 have?
2
The positive divisors of 43 are 1, 43, which is 2 factors in total.
7. How many positive whole-number factors (divisors) does 54 have?
8
The positive divisors of 54 are 1, 2, 3, 6, 9, 18, 27, 54, which is 8 factors in total.
8. 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.
9. How many positive whole-number factors (divisors) does 53 have?
2
The positive divisors of 53 are 1, 53, which is 2 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 56 have?
8
The positive divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, which is 8 factors in total.
12. 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.

12 questions · Seed 49 · Age guidance, not curriculum certification