GCF for 45, 120 and 525

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Greatest Common Factor of
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What's the Greatest Common Factor (GCF) of 45, 120 and 525?

Answer

GCF of 45, 120 and 525 is
15

Common factors: 1, 3, 5, 15

15 divides all three: 45 ÷ 15 = 3, 120 ÷ 15 = 8, 525 ÷ 15 = 35 — and 3, 8 and 35 have no factor but 1 common to all of them, so no larger number divides all three.

45 = 32 × 5

120 = 23 × 3 × 5

525 = 3 × 52 × 7

Prime45120525Lowest power
2—23——
332333
555525
7——7—

— = power 0: the prime is not a factor of this number, so it cannot be in the GCF.

GCF = 3 × 5 = 15

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GCF Table

1st2nd3rdGCF
4512051015
451205111
451205121
451205133
451205141
451205155
451205163
451205171
451205181
451205193
451205205
451205211
451205223
451205231
451205241
4512052515
451205261
451205271
451205283
451205291
451205305
451205313
451205321
451205331
451205343
451205355
451205361
451205373
451205381
451205391

FAQ

What's the Greatest Common Factor (GCF) of 45, 120 and 525?

GCF of 45, 120 and 525 is 15

What prime factors do 45, 120 and 525 share?

All three factorizations contain 3 × 5, and multiplying those shared primes gives 15 — exactly the greatest common factor.

Can you get the GCF of 45, 120 and 525 two numbers at a time?

Yes. The GCF of 45 and 120 is 15, and the GCF of 15 and 525 is 15 — the same answer, because the greatest common factor is associative and does not depend on the order of the three numbers.

How does the GCF simplify the ratio 45 : 120 : 525?

Divide every term by the GCF 15: 45 ÷ 15 = 3, 120 ÷ 15 = 8 and 525 ÷ 15 = 35. So 45 : 120 : 525 in lowest terms is 3 : 8 : 35, and no whole number other than 1 divides all three of those.

See Also