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GCF of 746/13, 178/422

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 746/13, 178/422 i.e 2/5486 easily. The following is the detailed procedure to determine the greatest common factor of fractions 746/13, 178/422.

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 746/13,178/422?

Given fractions are 746/13,178/422

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 746/13,178/422, numerators are 746,178

Denominators are 13,422

The GCF of 746,178 is 2 .

LCM of 13,422 is 5486.

The greatest common factor of 746/13,178/422 = [GCF of 746,178]/[LCM of 13,422]= 2/5486

Therefore, the GCF of 746/13,178/422 is 2/5486.

Greatest Common Factor of 746,178

To find the highest common factor of 746,178, we have to find the factors of both numbers and list the highest common factor.

The factors of 746 are 1, 2, 373, 746

The factors of 178 are 1, 2, 89, 178

The HCF of 746,178 is 2.

Lets's calculate GCF of 746,178

Greatest Common Factor (GCF) of 746,178 By Common Division

2 746, 178
373, 89

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

Greatest Common Factor of 746,178 By Matching Biggest Common Factor Method

Greatest Common Factor of 746,178 By Matching Biggest Common Factor Method

Now, list down the factors of 746

:

1,2,373,746

Now, list down the factors of 178

:

1,2,89,178

Greatest Common Factor

We found the factors 746,178 . The biggest common factor number is the GCF number.
So the greatest common factor 746,178 is 2.

Lets's calculate LCM of 13,422

Lowest Common Multiple of 13,422 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5486

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5486

Therefore, the GCF of Fractions 746/13,178/422 is 2/5486

Least Common Multiple of 13,422 with GCF Formula

Least Common Multiple of 13,422 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 13,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,422) = 1

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

GCF(13,422) x common factors =1 x 1 = 1

LCM(13,422) = ( 13 × 422 ) / 1

LCM(13,422) = 5486 / 1

LCM(13,422) = 5486


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FAQs on GCF of Fractions of 746/13, 178/422

1. What is the HCF of 746,178?

The HCF of 746,178 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 746/13, 178/422?

Answer: GCF of Numerators as per given numbers 746/13, 178/422 is

GCF of Numerators i.e. for 746,178 is 2

LCM of denominators i.e. for 13,422 is 5486.

Thus, GCF of Fractions is 2/5486.Finally, GCF of Fractions for 746/13, 178/422 is 2/5486.