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GCF (HCF) of 72 and 34

"Greatest Common Factor" Calculator

What is the Greatest Common Divisor of 72 and 34?

Answer

GCF (HCF) of 72 and 34 is

2

Common factors: 1, 2

2 divides both: 72 ÷ 2 = 36, 34 ÷ 2 = 17 — and 36 and 17 share no factor but 1, so no larger number divides both.

72 = 2³ × 3²

34 = 2 × 17

Prime	72	34	Lowest power
2	2³	2	2
3	3²	—	—
17	—	17	—

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

GCF = 2

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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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What is the GCF (HCF) of 72 and 34. The GCF of 72 and 34 is 2 — the biggest number that can divide both integers. Step-by-step GCF (GCD) calculation by factoring.

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GCF Table

Number 1	Number 2	GCF
72	19	1
72	20	4
72	21	3
72	22	2
72	23	1
72	24	24
72	25	1
72	26	2
72	27	9
72	28	4
72	29	1
72	30	6
72	31	1
72	32	8
72	33	3
72	34	2
72	35	1
72	36	36
72	37	1
72	38	2
72	39	3
72	40	8
72	41	1
72	42	6
72	43	1
72	44	4
72	45	9
72	46	2
72	47	1
72	48	24

FAQ

What is the Greatest Common Divisor of 72 and 34?

GCF (HCF) of 72 and 34 is 2

How to find the GCF of 72 and 34?

You can find the GCF of 72 and 34 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 72 and 34 is 2.

What prime factors do 72 and 34 share?

The prime factorizations of 72 and 34 have 2 in common, and multiplying those shared primes gives 2 — exactly the greatest common factor.

How does the GCF reduce the fraction 72/34?

Divide the numerator and the denominator by the GCF 2: 72 ÷ 2 = 36 and 34 ÷ 2 = 17. So 72/34 in lowest terms is 36/17.