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.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Counting positive divisors

Take your time. Show your thinking.

1. How many positive whole-number factors (divisors) does 39 have?
39 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 13 have?
13 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 25 have?
25 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 24 have?
24 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 30 have?
30 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 34 have?
34 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 21 have?
21 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 22 have?
22 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 59 have?
59 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 8 have?
8 h · Counting positive divisors

12 questions · Seed 47 · 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 39 have?
4
The positive divisors of 39 are 1, 3, 13, 39, which is 4 factors in total.
2. How many positive whole-number factors (divisors) does 13 have?
2
The positive divisors of 13 are 1, 13, which is 2 factors in total.
3. 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.
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 24 have?
8
The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, which is 8 factors in total.
6. How many positive whole-number factors (divisors) does 30 have?
8
The positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, 30, which is 8 factors in total.
7. 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.
8. 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.
9. How many positive whole-number factors (divisors) does 21 have?
4
The positive divisors of 21 are 1, 3, 7, 21, which is 4 factors in total.
10. 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.
11. 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.
12. 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.

12 questions · Seed 47 · 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 39 have?
39 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 13 have?
13 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 25 have?
25 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 24 have?
24 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 30 have?
30 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 34 have?
34 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 21 have?
21 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 22 have?
22 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 59 have?
59 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 8 have?
8 h · Counting positive divisors

12 questions · Seed 47 · 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 39 have?
4
The positive divisors of 39 are 1, 3, 13, 39, which is 4 factors in total.
2. How many positive whole-number factors (divisors) does 13 have?
2
The positive divisors of 13 are 1, 13, which is 2 factors in total.
3. 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.
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 24 have?
8
The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, which is 8 factors in total.
6. How many positive whole-number factors (divisors) does 30 have?
8
The positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, 30, which is 8 factors in total.
7. 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.
8. 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.
9. How many positive whole-number factors (divisors) does 21 have?
4
The positive divisors of 21 are 1, 3, 7, 21, which is 4 factors in total.
10. 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.
11. 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.
12. 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.

12 questions · Seed 47 · Age guidance, not curriculum certification