GCF for 45, 120 and 525

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

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

Answer

GCF of 45, 120 and 525 is
15

(Fifteen)

15 is the largest positive integer that divides 45, 120 and 525 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 45, 120 and 525 by Prime Factorization

Split all three numbers into prime factors, then keep every prime that appears in all three of them, each taken as many times as it appears in the poorest factorization. Multiplying what is left gives the greatest common factor:

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

All Prime Factors of 525: 3 × 5 × 5 × 7 (exponent form: 3 × 52 × 7)

Prime factor45120525Lowest power
2—23——
332333
555525
7——7—

GCF = 3 × 5 = 15

Checking the GCF of 45, 120 and 525 Two Numbers at a Time

The greatest common factor is associative, so three numbers can be handled as two pairs — and this is what makes the Euclidean algorithm usable here: run it on the first pair, then run it again on that result and the third number.

GCF(a, b, c) = GCF(GCF(a, b), c)

GCF(45, 120) = 15

GCF(15, 525) = 15

GCF(45, 120, 525) = 15

The answer checks out by division — all three quotients come out whole:

45 ÷ 15 = 3

120 ÷ 15 = 8

525 ÷ 15 = 35

3, 8 and 35 have no common factor left — that is what makes 15 the greatest one.

Related Calculations

See Also

About "Greatest Common Factor of 3 Numbers" Calculator

This calculator finds the Greatest Common Factor (GCF) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Greatest Common Factor (GCF) of 45, 120 and 525? (The answer is: 15). Enter the first number (e.g. '45'), the second (e.g. '120') and the third (e.g. '525'), then hit the 'Calculate' button.
The Greatest Common Factor of three numbers — also called the greatest common divisor (GCD) or highest common factor (HCF) — is the largest positive integer that divides all three of them with zero remainder
"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
and

GCF Table

Number 1Number 2Number 3GCF
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, and it is the check this page prints. 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