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 18 have?
18 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 31 have?
31 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 51 have?
51 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 48 have?
48 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 47 have?
47 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 52 have?
52 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 33 have?
33 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 60 have?
60 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 13 have?
13 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 15 have?
15 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 32 have?
32 h · Counting positive divisors

12 questions · Seed 46 · 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 18 have?
6
The positive divisors of 18 are 1, 2, 3, 6, 9, 18, which is 6 factors in total.
2. 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.
3. How many positive whole-number factors (divisors) does 51 have?
4
The positive divisors of 51 are 1, 3, 17, 51, which is 4 factors in total.
4. How many positive whole-number factors (divisors) does 48 have?
10
The positive divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, which is 10 factors in total.
5. 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.
6. 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.
7. How many positive whole-number factors (divisors) does 33 have?
4
The positive divisors of 33 are 1, 3, 11, 33, which is 4 factors in total.
8. 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.
9. 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.
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 15 have?
4
The positive divisors of 15 are 1, 3, 5, 15, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 32 have?
6
The positive divisors of 32 are 1, 2, 4, 8, 16, 32, which is 6 factors in total.

12 questions · Seed 46 · 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 18 have?
18 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 31 have?
31 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 51 have?
51 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 48 have?
48 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 47 have?
47 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 52 have?
52 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 33 have?
33 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 60 have?
60 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 13 have?
13 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 15 have?
15 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 32 have?
32 h · Counting positive divisors

12 questions · Seed 46 · 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 18 have?
6
The positive divisors of 18 are 1, 2, 3, 6, 9, 18, which is 6 factors in total.
2. 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.
3. How many positive whole-number factors (divisors) does 51 have?
4
The positive divisors of 51 are 1, 3, 17, 51, which is 4 factors in total.
4. How many positive whole-number factors (divisors) does 48 have?
10
The positive divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, which is 10 factors in total.
5. 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.
6. 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.
7. How many positive whole-number factors (divisors) does 33 have?
4
The positive divisors of 33 are 1, 3, 11, 33, which is 4 factors in total.
8. 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.
9. 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.
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 15 have?
4
The positive divisors of 15 are 1, 3, 5, 15, which is 4 factors in total.
12. How many positive whole-number factors (divisors) does 32 have?
6
The positive divisors of 32 are 1, 2, 4, 8, 16, 32, which is 6 factors in total.

12 questions · Seed 46 · Age guidance, not curriculum certification