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 31 have?
31 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 8 have?
8 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 56 have?
56 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 59 have?
59 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 22 have?
22 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 9 have?
9 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 26 have?
26 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 57 have?
57 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors

12 questions · Seed 104729 · 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 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 8 have?
4
The positive divisors of 8 are 1, 2, 4, 8, which is 4 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 56 have?
8
The positive divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, which is 8 factors in total.
5. 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.
6. 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.
7. 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.
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 26 have?
4
The positive divisors of 26 are 1, 2, 13, 26, which is 4 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 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 54 have?
8
The positive divisors of 54 are 1, 2, 3, 6, 9, 18, 27, 54, which is 8 factors in total.

12 questions · Seed 104729 · 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 31 have?
31 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 8 have?
8 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 56 have?
56 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 59 have?
59 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 22 have?
22 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 9 have?
9 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 26 have?
26 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 57 have?
57 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors

12 questions · Seed 104729 · 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 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 8 have?
4
The positive divisors of 8 are 1, 2, 4, 8, which is 4 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 56 have?
8
The positive divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, which is 8 factors in total.
5. 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.
6. 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.
7. 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.
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 26 have?
4
The positive divisors of 26 are 1, 2, 13, 26, which is 4 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 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 54 have?
8
The positive divisors of 54 are 1, 2, 3, 6, 9, 18, 27, 54, which is 8 factors in total.

12 questions · Seed 104729 · Age guidance, not curriculum certification