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 8 have?
8 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 53 have?
53 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 38 have?
38 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 60 have?
60 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 23 have?
23 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 49 have?
49 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 44 have?
44 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 25 have?
25 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 29 have?
29 h · Counting positive divisors

12 questions · Seed 104734 · 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 8 have?
4
The positive divisors of 8 are 1, 2, 4, 8, which is 4 factors in total.
2. 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.
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 38 have?
4
The positive divisors of 38 are 1, 2, 19, 38, which is 4 factors in total.
5. 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.
6. 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.
7. How many positive whole-number factors (divisors) does 60 have?
12
The positive divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, which is 12 factors in total.
8. 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.
9. 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.
10. How many positive whole-number factors (divisors) does 44 have?
6
The positive divisors of 44 are 1, 2, 4, 11, 22, 44, which is 6 factors in total.
11. 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.
12. 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.

12 questions · Seed 104734 · 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 8 have?
8 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 53 have?
53 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 38 have?
38 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 60 have?
60 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 23 have?
23 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 49 have?
49 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 44 have?
44 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 25 have?
25 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 29 have?
29 h · Counting positive divisors

12 questions · Seed 104734 · 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 8 have?
4
The positive divisors of 8 are 1, 2, 4, 8, which is 4 factors in total.
2. 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.
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 38 have?
4
The positive divisors of 38 are 1, 2, 19, 38, which is 4 factors in total.
5. 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.
6. 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.
7. How many positive whole-number factors (divisors) does 60 have?
12
The positive divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, which is 12 factors in total.
8. 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.
9. 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.
10. How many positive whole-number factors (divisors) does 44 have?
6
The positive divisors of 44 are 1, 2, 4, 11, 22, 44, which is 6 factors in total.
11. 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.
12. 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.

12 questions · Seed 104734 · Age guidance, not curriculum certification