GCF (HCF) of 70 and 105

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What is the Greatest Common Divisor of 70 and 105?

Answer

GCF (HCF) of 70 and 105 is
35

Common factors: 1, 5, 7, 35

35 divides both: 70 ÷ 35 = 2, 105 ÷ 35 = 3 — and 2 and 3 share no factor but 1, so no larger number divides both.

70 = 2 × 5 × 7

105 = 3 × 5 × 7

Prime70105Lowest power
22——
3—3—
5555
7777

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

GCF = 5 × 7 = 35

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GCF Table

Number 1Number 2GCF
70217
708010
708414
7010010
7010535
7011010
7013010
7015010
7016010
7017535
701855
702055
702155
7022010
702255
7023010
702355
7025010
702555
7026010
7027010
7028070
7029010
7030010
703055
7031010
7031535
7032010
703455
7037010

FAQ

What is the Greatest Common Divisor of 70 and 105?

GCF (HCF) of 70 and 105 is 35

How to find the GCF of 70 and 105?

You can find the GCF of 70 and 105 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 70 and 105 is 35.

What prime factors do 70 and 105 share?

The prime factorizations of 70 and 105 have 5 × 7 in common, and multiplying those shared primes gives 35 — exactly the greatest common factor.

How does the GCF reduce the fraction 70/105?

Divide the numerator and the denominator by the GCF 35: 70 ÷ 35 = 2 and 105 ÷ 35 = 3. So 70/105 in lowest terms is 2/3.

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