How to Find GCF of 117/748, 8242/7921?

GCF of 117/748, 8242/7921

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 117/748, 8242/7921 i.e 13/5924908 easily. The following is the detailed procedure to determine the greatest common factor of fractions 117/748, 8242/7921.

Enter two or more fractions separated by "commas"

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

What is the GCF of 117/748,8242/7921?

Given fractions are 117/748,8242/7921

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 117/748,8242/7921, numerators are 117,8242

Denominators are 748,7921

The GCF of 117,8242 is 13 .

LCM of 748,7921 is 5924908.

The greatest common factor of 117/748,8242/7921 = [GCF of 117,8242]/[LCM of 748,7921]= 13/5924908

Therefore, the GCF of 117/748,8242/7921 is 13/5924908.

Greatest Common Factor of 117,8242

To find the highest common factor of 117,8242, we have to find the factors of both numbers and list the highest common factor.

The factors of 117 are 1, 3, 9, 13, 39, 117

The factors of 8242 are 1, 2, 13, 26, 317, 634, 4121, 8242

The HCF of 117,8242 is 13.

Lets's calculate GCF of 117,8242

Greatest Common Factor (GCF) of 117,8242 By Common Division

13	117, 8242
	9, 634

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 117,8242 By Matching Biggest Common Factor Method

Now, list down the factors of 117

1,3,9,13,39,117

Now, list down the factors of 8242

1,2,13,26,317,634,4121,8242

Greatest Common Factor

We found the factors 117,8242 . The biggest common factor number is the GCF number.
So the greatest common factor 117,8242 is 13.

Lets's calculate LCM of 748,7921

Lowest Common Multiple of 748,7921 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5924908

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/5924908

Therefore, the GCF of Fractions 117/748,8242/7921 is 13/5924908

Least Common Multiple of 748,7921 with GCF Formula

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

We need to calculate greatest common factor of 748,7921 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(748,7921) = 1

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

GCF(748,7921) x common factors =1 x 1 = 1

LCM(748,7921) = ( 748 × 7921 ) / 1

LCM(748,7921) = 5924908 / 1

LCM(748,7921) = 5924908

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FAQs on GCF of Fractions of 117/748, 8242/7921

1. What is the HCF of 117,8242?

The HCF of 117,8242 is 13

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 117/748, 8242/7921?

Answer: GCF of Numerators as per given numbers 117/748, 8242/7921 is

GCF of Numerators i.e. for 117,8242 is 13

LCM of denominators i.e. for 748,7921 is 5924908.

Thus, GCF of Fractions is 13/5924908.Finally, GCF of Fractions for 117/748, 8242/7921 is 13/5924908.