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 41 have?
41 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 60 have?
60 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 35 have?
35 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 45 have?
45 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 23 have?
23 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 42 have?
42 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 52 have?
52 h · Counting positive divisors

12 questions · Seed 104731 · 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 41 have?
2
The positive divisors of 41 are 1, 41, which is 2 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 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.
5. 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.
6. How many positive whole-number factors (divisors) does 35 have?
4
The positive divisors of 35 are 1, 5, 7, 35, which is 4 factors in total.
7. How many positive whole-number factors (divisors) does 45 have?
6
The positive divisors of 45 are 1, 3, 5, 9, 15, 45, which is 6 factors in total.
8. 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.
9. 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.
10. How many positive whole-number factors (divisors) does 42 have?
8
The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42, which is 8 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 52 have?
6
The positive divisors of 52 are 1, 2, 4, 13, 26, 52, which is 6 factors in total.

12 questions · Seed 104731 · 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 41 have?
41 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 60 have?
60 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 35 have?
35 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 45 have?
45 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 23 have?
23 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 42 have?
42 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 52 have?
52 h · Counting positive divisors

12 questions · Seed 104731 · 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 41 have?
2
The positive divisors of 41 are 1, 41, which is 2 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 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.
5. 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.
6. How many positive whole-number factors (divisors) does 35 have?
4
The positive divisors of 35 are 1, 5, 7, 35, which is 4 factors in total.
7. How many positive whole-number factors (divisors) does 45 have?
6
The positive divisors of 45 are 1, 3, 5, 9, 15, 45, which is 6 factors in total.
8. 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.
9. 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.
10. How many positive whole-number factors (divisors) does 42 have?
8
The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42, which is 8 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 52 have?
6
The positive divisors of 52 are 1, 2, 4, 13, 26, 52, which is 6 factors in total.

12 questions · Seed 104731 · Age guidance, not curriculum certification