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 27 have?
27 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 26 have?
26 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 53 have?
53 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 13 have?
13 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 46 have?
46 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 29 have?
29 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 37 have?
37 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 43 have?
43 h · Counting positive divisors

12 questions · Seed 43 · 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 27 have?
4
The positive divisors of 27 are 1, 3, 9, 27, which is 4 factors in total.
2. 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.
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 53 have?
2
The positive divisors of 53 are 1, 53, which is 2 factors in total.
5. 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.
6. 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.
7. 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.
8. 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.
9. How many positive whole-number factors (divisors) does 46 have?
4
The positive divisors of 46 are 1, 2, 23, 46, which is 4 factors in total.
10. 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.
11. How many positive whole-number factors (divisors) does 37 have?
2
The positive divisors of 37 are 1, 37, which is 2 factors in total.
12. How many positive whole-number factors (divisors) does 43 have?
2
The positive divisors of 43 are 1, 43, which is 2 factors in total.

12 questions · Seed 43 · 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 27 have?
27 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 26 have?
26 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 53 have?
53 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 13 have?
13 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 15 have?
15 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 46 have?
46 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 29 have?
29 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 37 have?
37 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 43 have?
43 h · Counting positive divisors

12 questions · Seed 43 · 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 27 have?
4
The positive divisors of 27 are 1, 3, 9, 27, which is 4 factors in total.
2. 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.
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 53 have?
2
The positive divisors of 53 are 1, 53, which is 2 factors in total.
5. 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.
6. 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.
7. 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.
8. 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.
9. How many positive whole-number factors (divisors) does 46 have?
4
The positive divisors of 46 are 1, 2, 23, 46, which is 4 factors in total.
10. 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.
11. How many positive whole-number factors (divisors) does 37 have?
2
The positive divisors of 37 are 1, 37, which is 2 factors in total.
12. How many positive whole-number factors (divisors) does 43 have?
2
The positive divisors of 43 are 1, 43, which is 2 factors in total.

12 questions · Seed 43 · Age guidance, not curriculum certification