Working with numbers · Ages 12–13
Prime factorisation
Divide by 2 first, again and again, until you reach 1.
How to do it
Method
Divide by 2 first, again and again, until you reach 1
360 = 23 × 32 × 5
Another way
Factor tree
360 = 36 × 10 = 6 × 6 × 2 × 5
In full
To write a number as a product of primes, divide again and again: start with the smallest prime, 2, divide while you can, then try 3, 5, 7, … until the quotient is 1. 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1, so 360 = 23 × 32 × 5. Or draw a factor tree: 360 = 36 × 10, 36 = 6 × 6, 10 = 2 × 5, and each 6 = 2 × 3. The primes come out the same.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
672 = 2□ × 3□ × 7□
Fill in each blank
Show the answer and working
Answer: 5, 1, 1
Divide again and again: by 2 5 times, by 3 1 times, by 7 1 times.
Example 2
Which of these is 4320 written as a product of prime factors?
- A. 23 × 35 × 5
- B. 24 × 33 × 5
- C. 32 × 33 × 5
- D. 25 × 33 × 5
Choose the right answer
Show the answer and working
Answer: D. 25 × 33 × 5
4320 = 25 × 33 × 5: every factor is prime, and they multiply back to 4320.
Example 3
1872 = 24 × 32 × . What prime goes in ?
Show the answer and working
Answer: 13
Work out the known part first: 24 × 32 = 144. 1872 ÷ 144 = 13, a prime, so □ is 13.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Write 300 as a product of prime factors: 300 = 2□ × 3□ × 5□
Fill in each blank
Answer:
2.The largest prime factor of 504 is .
Answer:
3.Which of these is 720 written as a product of prime factors?
- A. 23 × 32 × 5
- B. 16 × 32 × 5
- C. 24 × 32 × 5
- D. 22 × 34 × 5
Choose the right answer
Answer:
4.Break 72 × 25 into prime factors: 72 × 25 = 2□ × 3□ × 5□
Fill in each blank
Answer:
5.Break 84 into prime factors by dividing again and again. Put the steps in order.
- A. 21 ÷ 3 = 7
- B. 7 ÷ 7 = 1
- C. 84 ÷ 2 = 42
- D. 42 ÷ 2 = 21
Write the letters in the right order
Answer:
All the answers
- 1. 2, 1, 2
- 2. 7
- 3. C. 24 × 32 × 5
- 4. 3, 2, 2
- 5. C → D → A → B
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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