Real numbers
Prime factorisation, HCF and LCM, and decimal expansions.
Learn with Kutty
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Every whole number is built from primes in exactly one way.
Look: 360 = 2 × 2 × 2 × 3 × 3 × 5.
✏️ Your turn!
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1Prime recipe of 140?
2HCF of 6 and 20?
3LCM of 6 and 20?
! Careful!
✗Mixing up HCF and LCM.
✓HCF is small (shared). LCM is big (everything).
✗Stopping before every piece is prime.
✓Keep splitting until all pieces are prime.
See the whole lesson on one page
Every whole number is built from primes in exactly one way.
Use the prime recipe to find HCF and LCM. HCF: the primes both numbers share. LCM: every prime either number needs.
Think of it like thisLike a fingerprint: 360 always breaks into 2 × 2 × 2 × 3 × 3 × 5, whichever way you start. No other number has that recipe.
- HCF
- Biggest number dividing both.
- LCM
- Smallest number both divide into.
Solved together
Find the HCF and LCM of 12 and 18.
Prime recipes.
12 = 2 × 2 × 318 = 2 × 3 × 3HCF: what they share.
2 × 3 = 6LCM: everything needed by either.
2 × 2 × 3 × 3 = 36
AnswerHCF 6, LCM 36.
For older learners and grown-ups: a little more
HCF × LCM = product of the two numbers (6 × 36 = 12 × 18). A fraction p/q in lowest terms has a terminating decimal exactly when q has no prime factors other than 2 and 5.
Now practise it
Kanakku makes new questions on real numbers every time. It shows the working and gives a hint when you are stuck.