How to Find GCF of 21/508, 10/582, 617/742?

GCF of 21/508, 10/582, 617/742

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 21/508, 10/582, 617/742 i.e 1/54844188 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/508, 10/582, 617/742.

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 21/508,10/582,617/742?

Given fractions are 21/508,10/582,617/742

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 21/508,10/582,617/742, numerators are 21,10,617

Denominators are 508,582,742

The GCF of 21,10,617 is 1 .

LCM of 508,582,742 is 54844188.

The greatest common factor of 21/508,10/582,617/742 = [GCF of 21,10,617]/[LCM of 508,582,742]= 1/54844188

Therefore, the GCF of 21/508,10/582,617/742 is 1/54844188.

Greatest Common Factor of 21,10,617

To find the highest common factor of 21,10,617, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 10 are 1, 2, 5, 10

The factors of 617 are 1, 617

The HCF of 21,10,617 is 1.

Lets's calculate GCF of 21,10,617

Greatest Common Factor (GCF) of 21,10,617 By Common Division

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

Greatest Common Factor of 21,10,617 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 617

1,617

Greatest Common Factor

We found the factors 21,10,617 . The biggest common factor number is the GCF number.
So the greatest common factor 21,10,617 is 1.

Lets's calculate LCM of 508,582,742

Lowest Common Multiple of 508,582,742 using Common Division

2	508, 582, 742
	254, 291, 371

∴ So the LCM of the given numbers is 2 x 254 x 291 x 371 = 54844188

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/54844188

Therefore, the GCF of Fractions 21/508,10/582,617/742 is 1/54844188

Least Common Multiple of 508,582,742 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 508,582,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(508,582,742) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(508,582,742) x common factors =2 x 2 = 4

LCM(508,582,742) = ( 508 × 582 × 742 ) / 4

LCM(508,582,742) = 219376752 / 4

LCM(508,582,742) = 54844188

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 21/508, 10/582, 617/742

1. What is the HCF of 21,10,617?

The HCF of 21,10,617 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 21/508, 10/582, 617/742?

Answer: GCF of Numerators as per given numbers 21/508, 10/582, 617/742 is

GCF of Numerators i.e. for 21,10,617 is 1

LCM of denominators i.e. for 508,582,742 is 54844188.

Thus, GCF of Fractions is 1/54844188.Finally, GCF of Fractions for 21/508, 10/582, 617/742 is 1/54844188.