Multiplying, dividing and mixed operations · Ages 9–10

Common factors and common multiples 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.The two smallest common multiples of 5 and 6 are and .
Fill in each blank
Answer:
2.How many common factors do 36 and 24 have?
Answer:
3.How many common factors do 18 and 54 have?
Answer:
4.The two smallest common multiples of 6 and 10 are and .
Fill in each blank
Answer:
5.The common factors of 63 and 84, smallest first: 1, , , .
Fill in each blank
Answer:
6.From 1 to 150, how many common multiples of 5 and 7 are there?
Answer:
7.From 1 to 78, how many common multiples of 2 and 9 are there?
Answer:

13.Route A leaves every 4 minutes and route B every 7 minutes. Both leave together at 7:00 a.m. In the 210 minutes after that (including minute 210), how many more times do they leave together?
Working:
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14.Tsz-ching goes to the library every 3 days and Ka-yee every 11 days. Both went today, the first time they went on the same day. After how many days, at the soonest, will they go on the same day for the third time?
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15.25 red pens and 20 blue pens are shared equally among some children, with none of either left. If there is more than 1 child, how many different numbers of children are possible?
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16.Ka-lok goes to the library every 4 days and Ka-yee every 5 days. Both went today, the first time they went on the same day. After how many days, at the soonest, will they go on the same day for the third time?
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17.Route A leaves every 4 minutes and route B every 7 minutes. Both leave together at 7:00 a.m. In the 167 minutes after that (including minute 167), how many more times do they leave together?
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18.6 red pens and 30 blue pens are shared equally among some children, with none of either left. If there is more than 1 child, how many different numbers of children are possible?
Working:
Answer:

Show the answers and working

Common factors and common multiples worksheet: Answers and working

1. 30, 60
List the multiples of 6 and check each one: is it also a multiple of 5?
List the multiples of 6 and pick those that are also multiples of 5: 30, 60, …
2. 6
List the factors of 36 and of 24, then ring the ones in both lists.
List both sets of factors: the ones in both are the common factors, which are just the factors of 12: 6 of them.
3. 6
List the factors of 18 and of 54, then ring the ones in both lists.
List both sets of factors: the ones in both are the common factors, which are just the factors of 18: 6 of them.
4. 30, 60
List the multiples of 10 and check each one: is it also a multiple of 6?
List the multiples of 10 and pick those that are also multiples of 6: 30, 60, …
5. 3, 7, 21
List the factors of 63 and of 84, then ring the ones in both, smallest first.
The highest common factor is 21, and the common factors are its factors: 1, 3, 7, 21.
6. 4
Find the smallest common multiple of 5 and 7 first: all the others are its multiples.
The common multiples are the multiples of 35: 150 ÷ 35 gives 4.
7. 4
Find the smallest common multiple of 2 and 9 first: all the others are its multiples.
The common multiples are the multiples of 18: 78 ÷ 18 gives 4.

8. False
A common factor must divide both. Try 18 ÷ 2 and 63 ÷ 2.
A common factor must divide both: check that 18 ÷ 2 and 63 ÷ 2 both leave no remainder.
9. D. 2
Try each option on both 10 and 6: it must divide both exactly.
10 ÷ 2 = 5 and 6 ÷ 2 = 3, no remainders: 2 is a common factor.
10. B. 4
Try each option on both 28 and 20: it must divide both exactly.
28 ÷ 4 = 7 and 20 ÷ 4 = 5, no remainders: 4 is a common factor.
11. True
A common factor must divide both. Try 15 ÷ 3 and 18 ÷ 3.
A common factor must divide both: check that 15 ÷ 3 and 18 ÷ 3 both leave no remainder.
12. False
A common multiple must be a multiple of both. Try 128 ÷ 8 and 128 ÷ 10.
A common multiple must be a multiple of both: 128 ÷ 8 and 128 ÷ 10 must both leave no remainder.

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

13. 7 times
They leave together at minutes that are multiples of both 4 and 7. Find the smallest first.
They leave together at the common multiples of 4 and 7, the multiples of 28: 210 ÷ 28 gives 7.
14. 66 days
They go on the same day at common multiples of 3 and 11. Today is already the first time; it asks for the third.
After today they meet on the common multiples of 3 and 11: after 33 days is the second time, after 66 days the third.
15. 1 number
The number of children must divide both 25 and 20: a common factor. Remember it's more than 1.
The number of children must be a common factor of 25 and 20, a factor of 5: 2 of them. Leaving out 1 gives 1.
16. 40 days
They go on the same day at common multiples of 4 and 5. Today is already the first time; it asks for the third.
After today they meet on the common multiples of 4 and 5: after 20 days is the second time, after 40 days the third.
17. 5 times
They leave together at minutes that are multiples of both 4 and 7. Find the smallest first.
They leave together at the common multiples of 4 and 7, the multiples of 28: 167 ÷ 28 gives 5.
18. 3 numbers
The number of children must divide both 6 and 30: a common factor. Remember it's more than 1.
The number of children must be a common factor of 6 and 30, a factor of 6: 4 of them. Leaving out 1 gives 3.

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