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 40 have?
40 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 21 have?
21 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 17 have?
17 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 6 have?
6 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 38 have?
38 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 42 have?
42 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 44 have?
44 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 55 have?
55 h · Counting positive divisors

12 questions · Seed 45 · 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 40 have?
8
The positive divisors of 40 are 1, 2, 4, 5, 8, 10, 20, 40, which is 8 factors in total.
2. 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.
3. 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.
4. How many positive whole-number factors (divisors) does 6 have?
4
The positive divisors of 6 are 1, 2, 3, 6, which is 4 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 38 have?
4
The positive divisors of 38 are 1, 2, 19, 38, which is 4 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 42 have?
8
The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42, which is 8 factors in total.
10. 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.
11. 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.
12. How many positive whole-number factors (divisors) does 55 have?
4
The positive divisors of 55 are 1, 5, 11, 55, which is 4 factors in total.

12 questions · Seed 45 · 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 40 have?
40 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 21 have?
21 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 17 have?
17 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 6 have?
6 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 38 have?
38 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 42 have?
42 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 44 have?
44 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 55 have?
55 h · Counting positive divisors

12 questions · Seed 45 · 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 40 have?
8
The positive divisors of 40 are 1, 2, 4, 5, 8, 10, 20, 40, which is 8 factors in total.
2. 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.
3. 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.
4. How many positive whole-number factors (divisors) does 6 have?
4
The positive divisors of 6 are 1, 2, 3, 6, which is 4 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 38 have?
4
The positive divisors of 38 are 1, 2, 19, 38, which is 4 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 42 have?
8
The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42, which is 8 factors in total.
10. 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.
11. 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.
12. How many positive whole-number factors (divisors) does 55 have?
4
The positive divisors of 55 are 1, 5, 11, 55, which is 4 factors in total.

12 questions · Seed 45 · Age guidance, not curriculum certification