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GCF of 852/311, 164/364

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 852/311, 164/364 i.e 4/113204 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/311, 164/364.

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 852/311,164/364?

Given fractions are 852/311,164/364

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 852/311,164/364, numerators are 852,164

Denominators are 311,364

The GCF of 852,164 is 4 .

LCM of 311,364 is 113204.

The greatest common factor of 852/311,164/364 = [GCF of 852,164]/[LCM of 311,364]= 4/113204

Therefore, the GCF of 852/311,164/364 is 4/113204.

Greatest Common Factor of 852,164

To find the highest common factor of 852,164, we have to find the factors of both numbers and list the highest common factor.

The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852

The factors of 164 are 1, 2, 4, 41, 82, 164

The HCF of 852,164 is 4.

Lets's calculate GCF of 852,164

Greatest Common Factor (GCF) of 852,164 By Common Division

2 852, 164
2 426, 82
213, 41

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 852,164 By Matching Biggest Common Factor Method

Greatest Common Factor of 852,164 By Matching Biggest Common Factor Method

Now, list down the factors of 852

:

1,2,3,4,6,12,71,142,213,284,426,852

Now, list down the factors of 164

:

1,2,4,41,82,164

Greatest Common Factor

We found the factors 852,164 . The biggest common factor number is the GCF number.
So the greatest common factor 852,164 is 4.

Lets's calculate LCM of 311,364

Lowest Common Multiple of 311,364 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 113204

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/113204

Therefore, the GCF of Fractions 852/311,164/364 is 4/113204

Least Common Multiple of 311,364 with GCF Formula

Least Common Multiple of 311,364 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 311,364 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(311,364) = 1

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

GCF(311,364) x common factors =1 x 1 = 1

LCM(311,364) = ( 311 × 364 ) / 1

LCM(311,364) = 113204 / 1

LCM(311,364) = 113204


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FAQs on GCF of Fractions of 852/311, 164/364

1. What is the HCF of 852,164?

The HCF of 852,164 is 4

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 852/311, 164/364?

Answer: GCF of Numerators as per given numbers 852/311, 164/364 is

GCF of Numerators i.e. for 852,164 is 4

LCM of denominators i.e. for 311,364 is 113204.

Thus, GCF of Fractions is 4/113204.Finally, GCF of Fractions for 852/311, 164/364 is 4/113204.