Reading it off the two prime lists
Take 84 and 96. Listing every factor takes too long.
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Step 1 of 5
- 12 = 2 × 2 × 3.
- 18 = 2 × 3 × 3.
- Pair a 2 with a 2, a 3 with a 3.
- One 2 and one 3 stay unpaired.
- Paired pieces: 2 × 3 = 6.
Pair the lists off
Write both prime lists. Pair each prime with the same prime in the other list. Each pair is a prime that both numbers have. Multiply the pairs. That is the HCF. A piece with no partner is left out.
Now 84 and 96:
- 84 = 2 × 2 × 3 × 7
- 96 = 2 × 2 × 2 × 2 × 2 × 3
- Pairs: 2, 2 and 3. HCF = 2 × 2 × 3 = 4 × 3 = 12.
- Left out: the 7, and three of the 2s in 96.