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Building Blocks of Numbers
Building Blocks of Numbers
Every whole number can be built from prime numbers - they're like the atoms of maths! Understanding factors (what divides into a number) and multiples (the times tables) helps with everything from simplifying fractions to solving real-world problems like tiling floors and scheduling events.
Factor: A number that divides exactly into another number with no remainder.
Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Mathematics glossary
- Factor
- A number that divides exactly into another number with no remainder. Example: Factors of 12 are 1, 2, 3, 4, 6, 12
- Multiple
- A number in the times table of another number. Example: Multiples of 5 are 5, 10, 15, 20, 25, 30...
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Exam Tips & Common Mistakes
Key Tips:
- Factor pairs: Always work systematically to avoid missing factors
- Prime factors: 1 is NOT a prime number (has only 1 factor, not 2)
- HCF: Cannot be larger than the smaller number
- LCM: Cannot be smaller than the larger number
- Check: HCF × LCM = product of the two numbers
Common Mistakes:
- ❌ Forgetting that 1 and the number itself are always factors
- ❌ Thinking 1 is prime (it's neither prime nor composite)
- ❌ Confusing HCF and LCM (HCF divides both, LCM is divisible by both)
- ❌ Not using systematic methods for large numbers
- ❌ Making arithmetic errors in factor trees
Memory Aids:
- FACTORS: "Divide IN" - factors divide into the number
- MULTIPLES: "Times table" - multiply the number
- HCF: "Highest that goes into both"
- LCM: "Lowest that both go into"
Now try it yourself
Quiz · Question 1 of 14
Which of these numbers is prime?
Tap an answer to check it