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GCF of 824/76, 165/742

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 824/76, 165/742 i.e 1/28196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 824/76, 165/742.

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 824/76,165/742?

Given fractions are 824/76,165/742

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 824/76,165/742, numerators are 824,165

Denominators are 76,742

The GCF of 824,165 is 1 .

LCM of 76,742 is 28196.

The greatest common factor of 824/76,165/742 = [GCF of 824,165]/[LCM of 76,742]= 1/28196

Therefore, the GCF of 824/76,165/742 is 1/28196.

Greatest Common Factor of 824,165

To find the highest common factor of 824,165, we have to find the factors of both numbers and list the highest common factor.

The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824

The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165

The HCF of 824,165 is 1.

Lets's calculate GCF of 824,165

Greatest Common Factor (GCF) of 824,165 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 824,165 By Matching Biggest Common Factor Method

Greatest Common Factor of 824,165 By Matching Biggest Common Factor Method

Now, list down the factors of 824

:

1,2,4,8,103,206,412,824

Now, list down the factors of 165

:

1,3,5,11,15,33,55,165

Greatest Common Factor

We found the factors 824,165 . The biggest common factor number is the GCF number.
So the greatest common factor 824,165 is 1.

Lets's calculate LCM of 76,742

Lowest Common Multiple of 76,742 using Common Division

2 76, 742
38, 371

∴ So the LCM of the given numbers is 2 x 38 x 371 = 28196

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28196

Therefore, the GCF of Fractions 824/76,165/742 is 1/28196

Least Common Multiple of 76,742 with GCF Formula

Least Common Multiple of 76,742 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 76,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,742) = 2

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

GCF(76,742) x common factors =2 x 1 = 2

LCM(76,742) = ( 76 × 742 ) / 2

LCM(76,742) = 56392 / 2

LCM(76,742) = 28196


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FAQs on GCF of Fractions of 824/76, 165/742

1. What is the HCF of 824,165?

The HCF of 824,165 is 1

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 824/76, 165/742?

Answer: GCF of Numerators as per given numbers 824/76, 165/742 is

GCF of Numerators i.e. for 824,165 is 1

LCM of denominators i.e. for 76,742 is 28196.

Thus, GCF of Fractions is 1/28196.Finally, GCF of Fractions for 824/76, 165/742 is 1/28196.