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GCF of 656/17, 456/962

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 656/17, 456/962 i.e 8/16354 easily. The following is the detailed procedure to determine the greatest common factor of fractions 656/17, 456/962.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 656/17,456/962?

Given fractions are 656/17,456/962

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 656/17,456/962, numerators are 656,456

Denominators are 17,962

The GCF of 656,456 is 8 .

LCM of 17,962 is 16354.

The greatest common factor of 656/17,456/962 = [GCF of 656,456]/[LCM of 17,962]= 8/16354

Therefore, the GCF of 656/17,456/962 is 8/16354.

Greatest Common Factor of 656,456

To find the highest common factor of 656,456, we have to find the factors of both numbers and list the highest common factor.

The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656

The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

The HCF of 656,456 is 8.

Lets's calculate GCF of 656,456

Greatest Common Factor (GCF) of 656,456 By Common Division

2 656, 456
2 328, 228
2 164, 114
82, 57

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 656,456 By Matching Biggest Common Factor Method

Greatest Common Factor of 656,456 By Matching Biggest Common Factor Method

Now, list down the factors of 656

:

1,2,4,8,16,41,82,164,328,656

Now, list down the factors of 456

:

1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456

Greatest Common Factor

We found the factors 656,456 . The biggest common factor number is the GCF number.
So the greatest common factor 656,456 is 8.

Lets's calculate LCM of 17,962

Lowest Common Multiple of 17,962 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 16354

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/16354

Therefore, the GCF of Fractions 656/17,456/962 is 8/16354

Least Common Multiple of 17,962 with GCF Formula

Least Common Multiple of 17,962 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 17,962 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,962) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(17,962) x common factors =1 x 1 = 1

LCM(17,962) = ( 17 × 962 ) / 1

LCM(17,962) = 16354 / 1

LCM(17,962) = 16354


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FAQs on GCF of Fractions of 656/17, 456/962

1. What is the HCF of 656,456?

The HCF of 656,456 is 8

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 656/17, 456/962?

Answer: GCF of Numerators as per given numbers 656/17, 456/962 is

GCF of Numerators i.e. for 656,456 is 8

LCM of denominators i.e. for 17,962 is 16354.

Thus, GCF of Fractions is 8/16354.Finally, GCF of Fractions for 656/17, 456/962 is 8/16354.