GCF for 36, 48 and 144

"Greatest Common Factor of 3 Numbers" Calculator
Greatest Common Factor of
,
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What's the Greatest Common Factor (GCF) of 36, 48 and 144?

Answer

GCF of 36, 48 and 144 is
12

(Twelve)

12 is the largest positive integer that divides 36, 48 and 144 without a remainder — every other common divisor of the three divides it too.

Finding the GCF of 36, 48 and 144 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

All Prime Factors of 144: 2 × 2 × 2 × 2 × 3 × 3 (exponent form: 24 × 32)

Prime factor3648144Lowest power
222242422
3323323

GCF = 2 × 2 × 3 = 12

Checking the GCF of 36, 48 and 144 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(36, 48) = 12

GCF(12, 144) = 12

GCF(36, 48, 144) = 12

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

36 ÷ 12 = 3

48 ÷ 12 = 4

144 ÷ 12 = 12

3, 4 and 12 have no common factor left — that is what makes 12 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 36, 48 and 144? (The answer is: 12). Enter the first number (e.g. '36'), the second (e.g. '48') and the third (e.g. '144'), 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
36481293
36481302
36481311
364813212
36481331
36481342
36481353
36481364
36481371
36481386
36481391
36481404
36481413
36481422
36481431
364814412
36481451
36481462
36481473
36481484
36481491
36481506
36481511
36481524
36481533
36481542
36481551
364815612
36481571
36481582

FAQ

What's the Greatest Common Factor (GCF) of 36, 48 and 144?

GCF of 36, 48 and 144 is 12

What prime factors do 36, 48 and 144 share?

All three factorizations contain 2 × 2 × 3, and multiplying those shared primes gives 12 — exactly the greatest common factor.

Can you get the GCF of 36, 48 and 144 two numbers at a time?

Yes, and it is the check this page prints. The GCF of 36 and 48 is 12, and the GCF of 12 and 144 is 12 — 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 36 : 48 : 144?

Divide every term by the GCF 12: 36 ÷ 12 = 3, 48 ÷ 12 = 4 and 144 ÷ 12 = 12. So 36 : 48 : 144 in lowest terms is 3 : 4 : 12, and no whole number other than 1 divides all three of those.

See Also