How to Find GCF of 31/537, 21/191, 409/179?

GCF of 31/537, 21/191, 409/179

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 31/537, 21/191, 409/179 i.e 1/102567 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/537, 21/191, 409/179.

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 31/537,21/191,409/179?

Given fractions are 31/537,21/191,409/179

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 31/537,21/191,409/179, numerators are 31,21,409

Denominators are 537,191,179

The GCF of 31,21,409 is 1 .

LCM of 537,191,179 is 102567.

The greatest common factor of 31/537,21/191,409/179 = [GCF of 31,21,409]/[LCM of 537,191,179]= 1/102567

Therefore, the GCF of 31/537,21/191,409/179 is 1/102567.

Greatest Common Factor of 31,21,409

To find the highest common factor of 31,21,409, we have to find the factors of both numbers and list the highest common factor.

The factors of 31 are 1, 31

The factors of 21 are 1, 3, 7, 21

The factors of 409 are 1, 409

The HCF of 31,21,409 is 1.

Lets's calculate GCF of 31,21,409

Greatest Common Factor (GCF) of 31,21,409 By Common Division

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

Greatest Common Factor of 31,21,409 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 409

1,409

Greatest Common Factor

We found the factors 31,21,409 . The biggest common factor number is the GCF number.
So the greatest common factor 31,21,409 is 1.

Lets's calculate LCM of 537,191,179

Lowest Common Multiple of 537,191,179 using Common Division

179	537, 191, 179
	3, 191, 1

∴ So the LCM of the given numbers is 179 x 3 x 191 x 1 = 102567

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/102567

Therefore, the GCF of Fractions 31/537,21/191,409/179 is 1/102567

Least Common Multiple of 537,191,179 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 537,191,179 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(537,191,179) = 1

common factors(in case of two or more numbers have common factors) = 179

GCF(537,191,179) x common factors =1 x 179 = 179

LCM(537,191,179) = ( 537 × 191 × 179 ) / 179

LCM(537,191,179) = 18359493 / 179

LCM(537,191,179) = 102567

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FAQs on GCF of Fractions of 31/537, 21/191, 409/179

1. What is the HCF of 31,21,409?

The HCF of 31,21,409 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 31/537, 21/191, 409/179?

Answer: GCF of Numerators as per given numbers 31/537, 21/191, 409/179 is

GCF of Numerators i.e. for 31,21,409 is 1

LCM of denominators i.e. for 537,191,179 is 102567.

Thus, GCF of Fractions is 1/102567.Finally, GCF of Fractions for 31/537, 21/191, 409/179 is 1/102567.