iStarSign inMath 8 · Unit 1: Integers · Cambridge Lower Secondary Maths Stage 8
1.1 Factors, multiples and primes
48 questions · e.g. Write 60 as a product of prime factors.
Questions
1. A factor tree for 250 starts with 2 × 125. Which shows how 125 is split to finish the tree?
- 125 → 5 × 20
- 125 → 5 × 25, then 25 → 5 × 5
- 125 → 5 × 25, then 25 → 5 × 10
- 125 → 25 × 25, then 25 → 5 × 5
2. Can you draw a different factor tree for 250 that starts with 2 × 125?
Check3. A factor tree for 250 starts with 25 × 10. How do 25 and 10 split?
- 25 → 2 × 5 and 10 → 5 × 5
- 25 → 5 × 5 and 10 → 5 × 5
- 25 → 5 × 5 and 10 → 2 × 5
- 25 → 5 × 5 and 10 → 2 × 2
4. Write 250 as a product of its prime factors.
Check5. Which is a correct factor tree for 300?
- 300 → 3 × 100; 100 → 10 × 10; each 10 → 2 × 5
- 300 → 3 × 100; 100 → 20 × 20
- 300 → 30 × 3; 30 → 5 × 5
- 300 → 3 × 100; 100 → 10 × 10; each 10 → 2 × 2
6. Which is a correct factor tree for 300 that does not start with 3 × 100?
- 300 → 50 × 6; 50 → 5 × 5; 6 → 2 × 3
- 300 → 30 × 10; 30 → 3 × 10; each 10 → 2 × 5
- 300 → 30 × 10; 30 → 3 × 5; 10 → 2 × 5
- 300 → 20 × 15; 20 → 2 × 5; 15 → 3 × 5
7. Write 300 as a product of prime numbers.
Check8. Write as a product of prime numbers: i 6, ii 30, iii 210
- 6 = 2 × 3; 30 = 2 × 3 × 5; 210 = 2 × 5 × 21
- 6 = 2 × 3; 30 = 2 × 3 × 5; 210 = 2 × 3 × 5 × 7
- 6 = 2 × 3; 30 = 3 × 10; 210 = 2 × 3 × 5 × 7
- 6 = 1 × 6; 30 = 2 × 15; 210 = 21 × 10
9. Parts i, ii and iii give 6, 30, 210, … What is the next number in this sequence?
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13. Which numbers end the branches of a factor tree for 8712?
Check14. Write 8712 as a product of prime numbers.
Check15. Write 96 as a product of its prime factors.
Check16. Write 97 as a product of its prime factors.
Check17. Write 98 as a product of its prime factors.
Check18. Write 99 as a product of its prime factors.
Check19. Write 70 as a product of prime numbers.
Check20. Write 70² as a product of prime numbers.
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