GCF (HCF) of 84 and 105
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What is the Greatest Common Divisor of 84 and 105?
Answer
GCF (HCF) of 84 and 105 is
21
Common factors: 1, 3, 7, 21
21 divides both: 84 ÷ 21 = 4, 105 ÷ 21 = 5 — and 4 and 5 share no factor but 1, so no larger number divides both.
84 = 22 × 3 × 7
105 = 3 × 5 × 7
| Prime | 84 | 105 | Lowest power |
|---|---|---|---|
| 2 | 22 | — | — |
| 3 | 3 | 3 | 3 |
| 5 | — | 5 | — |
| 7 | 7 | 7 | 7 |
— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.
GCF = 3 × 7 = 21
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See Also
- Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
- Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
- Least Common Multiple of 3 Numbers - Find the Least Common Multiple (LCM) of three numbers
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