Multiplying, dividing and mixed operations · Ages 9–10

Prime factorisation worksheet

Part of: Factors and multiples

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Multiplying, dividing and mixed operations · Ages 9–10

Numsprite
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Name:Date:Score:／48

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

1.117 = 3 × 3 ×
Answer:
2.385 = 5 × 7 ×
Answer:
3.When 186 is written as a product of primes, what is the biggest prime?
Answer:
4.When 200 is written as a product of primes, how many primes are there, counting repeats?
Answer:
5.132 = 2 × 2 × × (smallest first)
Fill in each blank
Answer:
6.36 = 2 × 2 × × (smallest first)
Fill in each blank
Answer:
7.When 270 is written as a product of primes, how many primes are there, counting repeats?
Answer:
8.When 183 is written as a product of primes, what is the biggest prime?
Answer:

9.Which of these is 60 written as a product of primes?
- A. 4 × 3 × 5
- B. 2 × 6 × 5
- C. 2 × 2 × 3 × 7
- D. 2 × 2 × 3 × 5
Choose the right answer
Answer:
10.Which of these is 132 written as a product of primes?
- A. 4 × 3 × 11
- B. 2 × 2 × 3 × 11
- C. 2 × 6 × 11
- D. 2 × 2 × 3 × 13
Choose the right answer
Answer:
11.60 = 2 × 2 × 3 × 5, and this is 60 written as a product of primes.
True or false?
Answer:
12.250 = 2 × 5 × 5 × 5, and this is 250 written as a product of primes.
True or false?
Answer:

13.A box holds 35 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:
14.A square's area = side × side. A square card has an area of 225 square centimetres, and its side is a whole number of centimetres. How long is its side?
Working:
Answer:
15.A 74 cm ribbon is cut into equal pieces with none left over, each a prime number of centimetres long. What is the longest each piece can be?
Working:
Answer:
16.195 small cubes, all the same, build exactly one solid cuboid. The numbers of cubes along its length, width and height are all prime, all different. Smallest first, they are , and cubes.
Fill in each blank
Working:
Answer:
17.A 216 cm ribbon is cut into equal pieces with none left over, each a prime number of centimetres long. What is the longest each piece can be?
Working:
Answer:
18.165 small cubes, all the same, build exactly one solid cuboid. The numbers of cubes along its length, width and height are all prime, all different. Smallest first, they are , and cubes.
Fill in each blank
Working:
Answer:

Show the answers and working

Prime factorisation worksheet: Answers and working

1. 13
Work out 117 ÷ 3 first, then divide that by 3.
117 ÷ 3 = 39, 39 ÷ 3 = 13, and 13 is prime.
2. 11
Work out 385 ÷ 5 first, then divide that by 7.
385 ÷ 5 = 77, 77 ÷ 7 = 11, and 11 is prime.
3. 31
Divide 186 by 2, 3, 5… until only primes are left.
Divide by 2, 3, 5… until only primes are left: the biggest is 31.
4. 5
Divide 200 by the smallest prime again and again, noting one prime each time it goes.
200 has 3 twos, 0 threes and 2 fives: 5 in all.
5. 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.
6. 3, 3
Divide 36 by 2 and by 2 again, then split what's left into two primes.
36 ÷ 2 ÷ 2 = 9, and 9 = 3 × 3, both prime.
7. 5
Divide 270 by the smallest prime again and again, noting one prime each time it goes.
270 has 1 twos, 3 threes and 1 fives: 5 in all.
8. 61
Divide 183 by 2, 3, 5… until only primes are left.
Divide by 2, 3, 5… until only primes are left: the biggest is 61.

9. D. 2 × 2 × 3 × 5
Check each option: every factor must be prime, and together they must make 60.
Every factor must be prime and they must make 60: 2 × 2 × 3 × 5.
10. B. 2 × 2 × 3 × 11
Check each option: every factor must be prime, and together they must make 132.
Every factor must be prime and they must make 132: 2 × 2 × 3 × 11.
11. True
Check two things: do they multiply to 60, and is every factor prime?
They must make 60, and every factor must be prime. 1 is not prime, so it can't be in it.
12. True
Check two things: do they multiply to 250, and is every factor prime?
They must make 250, and every factor must be prime. 1 is not prime, so it can't be in it.

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

13. 7 chocolates
Rows and number in a row are both prime and multiply to 35. Try dividing 35 by the smallest primes.
35 = 5 × 7, both prime: 5 rows of 7.
14. 15 cm
Write 225 as a product of primes, then split the primes into two matching groups.
225 = 3 × 5 × 3 × 5; split the primes into two matching groups, each 3 × 5 = 15: the side is 15 cm.
15. 37 cm
Each length must divide 74 and be prime. Write 74 as a product of primes first.
The length must be a prime factor of 74. Writing 74 as primes, the biggest is 37.
16. 3, 5, 13
The numbers along the three edges multiply to 195, all prime. Write 195 as a product of primes first.
The cubes in all = the number along the length × along the width × up the height, so write 195 as primes: 195 = 3 × 5 × 13.
17. 3 cm
Each length must divide 216 and be prime. Write 216 as a product of primes first.
The length must be a prime factor of 216. Writing 216 as primes, the biggest is 3.
18. 3, 5, 11
The numbers along the three edges multiply to 165, all prime. Write 165 as a product of primes first.
The cubes in all = the number along the length × along the width × up the height, so write 165 as primes: 165 = 3 × 5 × 11.

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