When a sum has several operations, the ORDER you do them in changes the answer completely. And every number has a hidden family of factors and multiples that unlocks HCF and LCM questions.
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When a sum mixes + − × ÷, you cannot just go left to right. Follow this order every time.
B O D M A S
B — Brackets
solve inside ( ) first
O — Of
"of" means multiply
D / M — Divide & Multiply
left to right, together
A / S — Add & Subtract
left to right, together, done last
Trap: Divide and Multiply are done together, left to right — NOT divide always before multiply. Same for Add and Subtract.
A factor divides a number exactly, with nothing left over. A multiple is what you get when you multiply a number by 1, 2, 3 …
🧩 Factors of 24
1, 2, 3, 4, 6, 8, 12, 24
Each of these divides 24 exactly.
➗ Multiples of 6
6, 12, 18, 24, 30 …
Each of these is 6 times a whole number.
Quick check: a prime number has exactly 2 factors — 1 and itself (like 7: only 1 and 7). A number with more than 2 factors is called composite (like 15: 1, 3, 5, 15).
HCF is the biggest number that divides two numbers exactly. LCM is the smallest number that both numbers divide into exactly.
🪜 The listing method
12 IMO-style questions. Use rough paper for the BODMAS sums! 🍀
