How to Find GCF of 89/272, 316/968?

GCF of 89/272, 316/968

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 89/272, 316/968 i.e 1/32912 easily. The following is the detailed procedure to determine the greatest common factor of fractions 89/272, 316/968.

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 89/272,316/968?

Given fractions are 89/272,316/968

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 89/272,316/968, numerators are 89,316

Denominators are 272,968

The GCF of 89,316 is 1 .

LCM of 272,968 is 32912.

The greatest common factor of 89/272,316/968 = [GCF of 89,316]/[LCM of 272,968]= 1/32912

Therefore, the GCF of 89/272,316/968 is 1/32912.

Greatest Common Factor of 89,316

To find the highest common factor of 89,316, we have to find the factors of both numbers and list the highest common factor.

The factors of 89 are 1, 89

The factors of 316 are 1, 2, 4, 79, 158, 316

The HCF of 89,316 is 1.

Lets's calculate GCF of 89,316

Greatest Common Factor (GCF) of 89,316 By Common Division

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

Greatest Common Factor of 89,316 By Matching Biggest Common Factor Method

Now, list down the factors of 89

1,89

Now, list down the factors of 316

1,2,4,79,158,316

Greatest Common Factor

We found the factors 89,316 . The biggest common factor number is the GCF number.
So the greatest common factor 89,316 is 1.

Lets's calculate LCM of 272,968

Lowest Common Multiple of 272,968 using Common Division

2	272, 968
2	136, 484
2	68, 242
	34, 121

∴ So the LCM of the given numbers is 2 x 2 x 2 x 34 x 121 = 32912

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32912

Therefore, the GCF of Fractions 89/272,316/968 is 1/32912

Least Common Multiple of 272,968 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 272,968 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(272,968) = 8

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

GCF(272,968) x common factors =8 x 1 = 8

LCM(272,968) = ( 272 × 968 ) / 8

LCM(272,968) = 263296 / 8

LCM(272,968) = 32912

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FAQs on GCF of Fractions of 89/272, 316/968

1. What is the HCF of 89,316?

The HCF of 89,316 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 89/272, 316/968?

Answer: GCF of Numerators as per given numbers 89/272, 316/968 is

GCF of Numerators i.e. for 89,316 is 1

LCM of denominators i.e. for 272,968 is 32912.

Thus, GCF of Fractions is 1/32912.Finally, GCF of Fractions for 89/272, 316/968 is 1/32912.