Multiplying, dividing and mixed operations · Ages 9–10
Factors and multiples worksheet
Covers: Multiples, Factors, Prime and composite numbers, Prime factorisation, Common factors and common multiples, Highest common factor, Lowest (least) common multiple (L.C.M.)
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Factors and multiples worksheet
Multiplying, dividing and mixed operations · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Multiples of 8: 8, , , , …
Fill in each blank
Answer:
2.From 28 to 61 (including both), how many multiples of 11 are there?
Answer:
3.What is the second largest factor of 159?
Answer:
4.Next prime after 47 = ?
Answer:
5.Least prime factor of 62 = ?
Answer:
6.132 = 2 × 2 × × (smallest first)
Fill in each blank
Answer:
7.The two smallest common multiples of 3 and 8 are and .
Fill in each blank
Answer:
8.How many common factors do 60 and 80 have?
Answer:
9.H.C.F. of 45 and 36 = ?
Answer:
10.L.C.M. of 15 and 2 = ?
Answer:
Part B: Choose, or true or false (2 marks each)
11.Which of these is a factor of 44?
- A. 12
- B. 11
- C. 6
- D. 88
Choose the right answer
Answer:
12.Which of these is 156 written as a product of primes?
- A. 4 × 3 × 13
- B. 2 × 6 × 13
- C. 2 × 2 × 3 × 17
- D. 2 × 2 × 3 × 13
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A path is 60 m long. Trees are planted every 3 m from the start, including both ends. How many trees are planted?
Working:
Answer:
14.176 chocolates are laid out in a rectangle, with 5 more in each row than there are rows. How many are in each row?
Working:
Answer:
15.A box holds 95 chocolates in a rectangle. The number of rows and the number in each row are both prime, with more in each row than there are rows. How many are in each row?
Working:
Answer:
16.60 red pens and 36 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:
17.Mr Lee has 96 pencils and 84 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?
Working:
Answer:
18.Ming goes swimming every 4 days and May every 9 days. They both swim today. In how many days will they next swim on the same day?
Working:
Answer:
Show the answers and working
Factors and multiples worksheet: Answers and working
Part A: Working out and filling in
1. 16, 24, 32
The multiples of 8 are 8 times 1, times 2, times 3, … Work them out in turn.
8 times 1, 2, 3, 4: 8, 16, 24, 32.
2. 3
Count the multiples of 11 from 1 to 61 first, then think what to do with those below 28.
The multiples of 11 from 1 to 61, subtract those below 28: 3.
3. 53
The second largest factor pairs with the second smallest. Find the smallest factor above 1 first.
Factors come in pairs: the largest, 159, pairs with 1, and the second largest with the second smallest, 3. So it is 159 ÷ 3 = 53.
4. Next prime after 47 = 53
The next prime after 47: 48: 48 is even, 48 ÷ 2 = 24; 49: 49 ÷ 7 = 7; 50: 50 is even, 50 ÷ 2 = 25; 51: its digits add up to 5 + 1 = 6, a multiple of 3, 51 ÷ 3 = 17; 52: 52 is even, 52 ÷ 2 = 26; 53 divides by none of 2, 3, 5, 7, so it's prime — the answer is 53
5. Least prime factor of 62 = 2
Smallest prime factor of 62: try 2, 3, 5, 7 in turn: 62 is even, 62 ÷ 2 = 31, so the smallest prime factor is 2
6. 3, 11
Divide 132 by 2 and by 2 again, then split what's left into two primes.
132 ÷ 2 ÷ 2 = 33, and 33 = 3 × 11, both prime.
7. 24, 48
List the multiples of 8 and check each one: is it also a multiple of 3?
List the multiples of 8 and pick those that are also multiples of 3: 24, 48, …
8. 6
List the factors of 60 and of 80, 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 20: 6 of them.
9. H.C.F. of 45 and 36 = 9
H.C.F. of 45 and 36: by short division, 45 and 36 ÷ 3 → 15 and 12; 15 and 12 ÷ 3 → 5 and 4; 5 and 4 share no factor but 1. Multiply the divisors: 3 × 3 = 9, so the H.C.F. is 9
10. L.C.M. of 15 and 2 = 30
L.C.M. of 15 and 2: 15 and 2 share no factor but 1, so the L.C.M. is the two multiplied: 15 × 2 = 30
Part B: Choose, or true or false
11. B. 11
Try dividing 44 by each option and see which goes exactly.
44 ÷ 11 = 4 with no remainder, so 11 is a factor of 44.
12. D. 2 × 2 × 3 × 13
Check each option: every factor must be prime, and together they must make 156.
Every factor must be prime and they must make 156: 2 × 2 × 3 × 13.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 21 trees
Work out how many 3 m gaps fit in 60 m, then think: with trees at both ends, more trees or more gaps?
Trees stand at 0 m and every multiple of 3: 60 ÷ 3 = 20 gaps, and one more tree than gaps: 21.
14. 16 chocolates
Rows × number in a row = 176. Go through 176's factor pairs for the pair 5 apart.
The rows and the number in a row are a factor pair of 176, 5 apart: 11 × 16 = 176, so 16 a row.
15. 19 chocolates
Rows and number in a row are both prime and multiply to 95. Try dividing 95 by the smallest primes.
95 = 5 × 19, both prime: 5 rows of 19.
16. 5 numbers
The number of children must divide both 60 and 36: a common factor. Remember it's more than 1.
The number of children must be a common factor of 60 and 36, a factor of 12: 6 of them. Leaving out 1 gives 5.
17. Mr Lee has 96 pencils and 84 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: 12 pupils)
The H.C.F. of 96 and 84 is 12
18. Ming goes swimming every 4 days and May every 9 days. They both swim today. In how many days will they next swim on the same day? (Answer: 36 days)
The L.C.M. of 4 and 9 is 36
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