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GCF of 493/20, 676/146

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 493/20, 676/146 i.e 1/1460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 493/20, 676/146.

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 493/20,676/146?

Given fractions are 493/20,676/146

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 493/20,676/146, numerators are 493,676

Denominators are 20,146

The GCF of 493,676 is 1 .

LCM of 20,146 is 1460.

The greatest common factor of 493/20,676/146 = [GCF of 493,676]/[LCM of 20,146]= 1/1460

Therefore, the GCF of 493/20,676/146 is 1/1460.

Greatest Common Factor of 493,676

To find the highest common factor of 493,676, we have to find the factors of both numbers and list the highest common factor.

The factors of 493 are 1, 17, 29, 493

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676

The HCF of 493,676 is 1.

Lets's calculate GCF of 493,676

Greatest Common Factor (GCF) of 493,676 By Common Division

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

Greatest Common Factor of 493,676 By Matching Biggest Common Factor Method

Greatest Common Factor of 493,676 By Matching Biggest Common Factor Method

Now, list down the factors of 493

:

1,17,29,493

Now, list down the factors of 676

:

1,2,4,13,26,52,169,338,676

Greatest Common Factor

We found the factors 493,676 . The biggest common factor number is the GCF number.
So the greatest common factor 493,676 is 1.

Lets's calculate LCM of 20,146

Lowest Common Multiple of 20,146 using Common Division

2 20, 146
10, 73

∴ So the LCM of the given numbers is 2 x 10 x 73 = 1460

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1460

Therefore, the GCF of Fractions 493/20,676/146 is 1/1460

Least Common Multiple of 20,146 with GCF Formula

Least Common Multiple of 20,146 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 20,146 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,146) = 2

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

GCF(20,146) x common factors =2 x 1 = 2

LCM(20,146) = ( 20 × 146 ) / 2

LCM(20,146) = 2920 / 2

LCM(20,146) = 1460


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FAQs on GCF of Fractions of 493/20, 676/146

1. What is the HCF of 493,676?

The HCF of 493,676 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 493/20, 676/146?

Answer: GCF of Numerators as per given numbers 493/20, 676/146 is

GCF of Numerators i.e. for 493,676 is 1

LCM of denominators i.e. for 20,146 is 1460.

Thus, GCF of Fractions is 1/1460.Finally, GCF of Fractions for 493/20, 676/146 is 1/1460.