Highest common factor worksheet

Part A: Working out and filling in

1. 1. H.C.F. of 91 and 65 = 13

   H.C.F. of 91 and 65: by short division, 91 and 65 ÷ 13 → 7 and 5; 7 and 5 share no factor but 1, so the H.C.F. is the divisor, 13

2. 2. H.C.F. of 6 and 24 = 6

   H.C.F. of 6 and 24: by short division, 6 and 24 ÷ 2 → 3 and 12; 3 and 12 ÷ 3 → 1 and 4; 1 and 4 share no factor but 1. Multiply the divisors: 2 × 3 = 6, so the H.C.F. is 6

3. 3. H.C.F. of 6 and 9 = 3

   H.C.F. of 6 and 9: by short division, 6 and 9 ÷ 3 → 2 and 3; 2 and 3 share no factor but 1, so the H.C.F. is the divisor, 3

4. 4. H.C.F. of 40 and 45 = 5

   H.C.F. of 40 and 45: by short division, 40 and 45 ÷ 5 → 8 and 9; 8 and 9 share no factor but 1, so the H.C.F. is the divisor, 5

5. 5. H.C.F. of 15 and 5 = 5

   H.C.F. of 15 and 5: by short division, 15 and 5 ÷ 5 → 3 and 1; 3 and 1 share no factor but 1, so the H.C.F. is the divisor, 5

6. 6. H.C.F. of 10 and 6 = 2

   H.C.F. of 10 and 6: by short division, 10 and 6 ÷ 2 → 5 and 3; 5 and 3 share no factor but 1, so the H.C.F. is the divisor, 2

7. 7. H.C.F. of 30 and 45 = 15

   H.C.F. of 30 and 45: by short division, 30 and 45 ÷ 3 → 10 and 15; 10 and 15 ÷ 5 → 2 and 3; 2 and 3 share no factor but 1. Multiply the divisors: 3 × 5 = 15, so the H.C.F. is 15

8. 8. H.C.F. of 9 and 18 = 9

   H.C.F. of 9 and 18: by short division, 9 and 18 ÷ 3 → 3 and 6; 3 and 6 ÷ 3 → 1 and 2; 1 and 2 share no factor but 1. Multiply the divisors: 3 × 3 = 9, so the H.C.F. is 9

9. 9. H.C.F. of 15 and 12 = 3

   H.C.F. of 15 and 12: by short division, 15 and 12 ÷ 3 → 5 and 4; 5 and 4 share no factor but 1, so the H.C.F. is the divisor, 3

10. 10. H.C.F. of 28 and 70 = 14

    H.C.F. of 28 and 70: by short division, 28 and 70 ÷ 2 → 14 and 35; 14 and 35 ÷ 7 → 2 and 5; 2 and 5 share no factor but 1. Multiply the divisors: 2 × 7 = 14, so the H.C.F. is 14

11. 11. H.C.F. of 98 and 14 = 14

    H.C.F. of 98 and 14: by short division, 98 and 14 ÷ 2 → 49 and 7; 49 and 7 ÷ 7 → 7 and 1; 7 and 1 share no factor but 1. Multiply the divisors: 2 × 7 = 14, so the H.C.F. is 14

12. 12. H.C.F. of 48 and 6 = 6

    H.C.F. of 48 and 6: by short division, 48 and 6 ÷ 2 → 24 and 3; 24 and 3 ÷ 3 → 8 and 1; 8 and 1 share no factor but 1. Multiply the divisors: 2 × 3 = 6, so the H.C.F. is 6

Part B: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. Mr Lee has 44 pencils and 55 notebooks to share among some pupils. Each pupil must get the same number of pencils and the same number of notebooks, with none left over. What is the greatest number of pupils he can share them among? (Answer: 11 pupils)

   The H.C.F. of 44 and 55 is 11

2. 14. A rectangular card 20 cm long and 12 cm wide is cut into equal squares with nothing left over. What is the longest each square's side can be, in centimetres? (Answer: 4 cm)

   The H.C.F. of 20 and 12 is 4

3. 15. A rectangular card 20 cm long and 15 cm wide is cut into equal squares with nothing left over. What is the longest each square's side can be, in centimetres? (Answer: 5 cm)

   The H.C.F. of 20 and 15 is 5

4. 16. A florist has 30 red roses and 70 white roses to make into bunches. Every bunch has the same number of red roses and the same number of white roses, and all the roses are used. What is the greatest number of bunches the florist can make? (Answer: 10 bunches)

   The H.C.F. of 30 and 70 is 10

5. 17. A florist has 8 red roses and 36 white roses to make into bunches. Every bunch has the same number of red roses and the same number of white roses, and all the roses are used. What is the greatest number of bunches the florist can make? (Answer: 4 bunches)

   The H.C.F. of 8 and 36 is 4

6. 18. Two ribbons, 133 cm and 76 cm long, are cut into pieces of equal length with nothing left over. What is the longest each piece can be, in centimetres? (Answer: 19 cm)

   The H.C.F. of 133 and 76 is 19