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 15 have?
15 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 45 have?
45 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 50 have?
50 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 7 have?
7 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 44 have?
44 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 17 have?
17 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 21 have?
21 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 43 have?
43 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 35 have?
35 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 18 have?
18 h · Counting positive divisors

12 questions · Seed 42 · 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 15 have?
4
The positive divisors of 15 are 1, 3, 5, 15, which is 4 factors in total.
2. 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.
3. How many positive whole-number factors (divisors) does 50 have?
6
The positive divisors of 50 are 1, 2, 5, 10, 25, 50, which is 6 factors in total.
4. 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.
5. How many positive whole-number factors (divisors) does 7 have?
2
The positive divisors of 7 are 1, 7, which is 2 factors in total.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 42 · 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 15 have?
15 h · Counting positive divisors
2. How many positive whole-number factors (divisors) does 45 have?
45 h · Counting positive divisors
3. How many positive whole-number factors (divisors) does 50 have?
50 h · Counting positive divisors
4. How many positive whole-number factors (divisors) does 28 have?
28 h · Counting positive divisors
5. How many positive whole-number factors (divisors) does 7 have?
7 h · Counting positive divisors
6. How many positive whole-number factors (divisors) does 44 have?
44 h · Counting positive divisors
7. How many positive whole-number factors (divisors) does 54 have?
54 h · Counting positive divisors
8. How many positive whole-number factors (divisors) does 17 have?
17 h · Counting positive divisors
9. How many positive whole-number factors (divisors) does 21 have?
21 h · Counting positive divisors
10. How many positive whole-number factors (divisors) does 43 have?
43 h · Counting positive divisors
11. How many positive whole-number factors (divisors) does 35 have?
35 h · Counting positive divisors
12. How many positive whole-number factors (divisors) does 18 have?
18 h · Counting positive divisors

12 questions · Seed 42 · 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 15 have?
4
The positive divisors of 15 are 1, 3, 5, 15, which is 4 factors in total.
2. 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.
3. How many positive whole-number factors (divisors) does 50 have?
6
The positive divisors of 50 are 1, 2, 5, 10, 25, 50, which is 6 factors in total.
4. 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.
5. How many positive whole-number factors (divisors) does 7 have?
2
The positive divisors of 7 are 1, 7, which is 2 factors in total.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 42 · Age guidance, not curriculum certification