Multiplying, dividing and mixed operations · Ages 9–10

Factors worksheet

Part of: Factors and multiples

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Multiplying, dividing and mixed operations · Ages 9–10

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.70 ÷ 10 = with no remainder, so 10 is a factor of 70.
Answer:
2.How many factors does 30 have?
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3.Finding the factors of 60 in pairs: 1 × 60, 2 × , 3 × , 4 × , …
Fill in each blank
Answer:
4.How many factors does 56 have?
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5.Finding the factors of 84 in pairs: 1 × 84, 2 × , 3 × , 4 × , …
Fill in each blank
Answer:
6.What is the second largest factor of 50?
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7.What is the second largest factor of 143?
Answer:

13.20 chocolates are laid out in a rectangle, with 1 more in each row than there are rows. How many are in each row?
Working:
Answer:
14.A 99 cm ribbon is cut into equal pieces with none left. Each piece is a whole number of cm, at least 2 cm, and there are at least 2 pieces. The shortest each piece can be is cm, and the longest is cm.
Fill in each blank
Working:
Answer:
15.28 chairs are set out in a rectangle, the same number in each row, at least 2 rows and at least 2 chairs a row. A different number of rows counts as a different way. How many ways are there?
Working:
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16.192 chocolates are laid out in a rectangle, with 4 more in each row than there are rows. How many are in each row?
Working:
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17.100 chairs are set out in a rectangle, the same number in each row, at least 2 rows and at least 2 chairs a row. A different number of rows counts as a different way. How many ways are there?
Working:
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18.A 22 cm ribbon is cut into equal pieces with none left. Each piece is a whole number of cm, at least 2 cm, and there are at least 2 pieces. The shortest each piece can be is cm, and the longest is cm.
Fill in each blank
Working:
Answer:

Show the answers and working

Factors worksheet: Answers and working

1. 7
Think what 10 must be multiplied by to make 70.
10 × 7 = 70, so 70 ÷ 10 = 7.
2. 8
Find 30's factors in pairs starting from 1, stop when the pair meets, then count them.
Find the factors of 30 in pairs from 1 until the pair meets: 8 in all.
3. 30, 20, 15
Each pair must multiply to 60. Start with 60 ÷ 2.
60 ÷ 2 = 30, 60 ÷ 3 = 20, 60 ÷ 4 = 15: each pair multiplies to 60.
4. 8
Find 56's factors in pairs starting from 1, stop when the pair meets, then count them.
Find the factors of 56 in pairs from 1 until the pair meets: 8 in all.
5. 42, 28, 21
Each pair must multiply to 84. Start with 84 ÷ 2.
84 ÷ 2 = 42, 84 ÷ 3 = 28, 84 ÷ 4 = 21: each pair multiplies to 84.
6. 25
The second largest factor pairs with the second smallest. Find the smallest factor above 1 first.
Factors come in pairs: the largest, 50, pairs with 1, and the second largest with the second smallest, 2. So it is 50 ÷ 2 = 25.
7. 13
The second largest factor pairs with the second smallest. Find the smallest factor above 1 first.
Factors come in pairs: the largest, 143, pairs with 1, and the second largest with the second smallest, 11. So it is 143 ÷ 11 = 13.

8. True
Try 42 ÷ 3 and see whether it divides exactly.
42 ÷ 3 = 14 remainder 0. Only if it divides exactly is 3 a factor of 42.
9. True
Try 88 ÷ 8 and see whether it divides exactly.
88 ÷ 8 = 11 remainder 0. Only if it divides exactly is 8 a factor of 88.
10. A. 5 is a factor of 45
5 divides 45 exactly. Think which is then the factor and which the multiple.
5 divides 45 exactly, so 5 is a factor of 45 and 45 is a multiple of 5.
11. B. 12
Try dividing 36 by each option and see which goes exactly.
36 ÷ 12 = 3 with no remainder, so 12 is a factor of 36.
12. B. 3
Try dividing 21 by each option and see which goes exactly.
21 ÷ 3 = 7 with no remainder, so 3 is a factor of 21.

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

13. 5 chocolates
Rows × number in a row = 20. Go through 20's factor pairs for the pair 1 apart.
The rows and the number in a row are a factor pair of 20, 1 apart: 4 × 5 = 20, so 5 a row.
14. 3, 33
Each piece's length must divide 99 exactly. Find the smallest factor above 1 first.
Each piece's length is a factor of 99. The smallest factor above 1 is 3; with at least 2 pieces, the longest is 99 ÷ 3 = 33.
15. 4 ways
The number of rows must divide 28 exactly. Find all the factors of 28 in pairs first.
The number of rows is a factor of 28. 28 has 6 factors; leaving out 1 and 28 (one row, or one chair a row) gives 4.
16. 16 chocolates
Rows × number in a row = 192. Go through 192's factor pairs for the pair 4 apart.
The rows and the number in a row are a factor pair of 192, 4 apart: 12 × 16 = 192, so 16 a row.
17. 7 ways
The number of rows must divide 100 exactly. Find all the factors of 100 in pairs first.
The number of rows is a factor of 100. 100 has 9 factors; leaving out 1 and 100 (one row, or one chair a row) gives 7.
18. 2, 11
Each piece's length must divide 22 exactly. Find the smallest factor above 1 first.
Each piece's length is a factor of 22. The smallest factor above 1 is 2; with at least 2 pieces, the longest is 22 ÷ 2 = 11.

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