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GCF of 442/208, 656/179

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 442/208, 656/179 i.e 2/37232 easily. The following is the detailed procedure to determine the greatest common factor of fractions 442/208, 656/179.

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 442/208,656/179?

Given fractions are 442/208,656/179

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 442/208,656/179, numerators are 442,656

Denominators are 208,179

The GCF of 442,656 is 2 .

LCM of 208,179 is 37232.

The greatest common factor of 442/208,656/179 = [GCF of 442,656]/[LCM of 208,179]= 2/37232

Therefore, the GCF of 442/208,656/179 is 2/37232.

Greatest Common Factor of 442,656

To find the highest common factor of 442,656, we have to find the factors of both numbers and list the highest common factor.

The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442

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

The HCF of 442,656 is 2.

Lets's calculate GCF of 442,656

Greatest Common Factor (GCF) of 442,656 By Common Division

2 442, 656
221, 328

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

Greatest Common Factor of 442,656 By Matching Biggest Common Factor Method

Greatest Common Factor of 442,656 By Matching Biggest Common Factor Method

Now, list down the factors of 442

:

1,2,13,17,26,34,221,442

Now, list down the factors of 656

:

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

Greatest Common Factor

We found the factors 442,656 . The biggest common factor number is the GCF number.
So the greatest common factor 442,656 is 2.

Lets's calculate LCM of 208,179

Lowest Common Multiple of 208,179 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 37232

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/37232

Therefore, the GCF of Fractions 442/208,656/179 is 2/37232

Least Common Multiple of 208,179 with GCF Formula

Least Common Multiple of 208,179 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 208,179 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(208,179) = 1

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

GCF(208,179) x common factors =1 x 1 = 1

LCM(208,179) = ( 208 × 179 ) / 1

LCM(208,179) = 37232 / 1

LCM(208,179) = 37232


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FAQs on GCF of Fractions of 442/208, 656/179

1. What is the HCF of 442,656?

The HCF of 442,656 is 2

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 442/208, 656/179?

Answer: GCF of Numerators as per given numbers 442/208, 656/179 is

GCF of Numerators i.e. for 442,656 is 2

LCM of denominators i.e. for 208,179 is 37232.

Thus, GCF of Fractions is 2/37232.Finally, GCF of Fractions for 442/208, 656/179 is 2/37232.