How to Find GCF of 546/499, 7631/7697?

GCF of 546/499, 7631/7697

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 546/499, 7631/7697 i.e 13/3840803 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/499, 7631/7697.

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 546/499,7631/7697?

Given fractions are 546/499,7631/7697

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 546/499,7631/7697, numerators are 546,7631

Denominators are 499,7697

The GCF of 546,7631 is 13 .

LCM of 499,7697 is 3840803.

The greatest common factor of 546/499,7631/7697 = [GCF of 546,7631]/[LCM of 499,7697]= 13/3840803

Therefore, the GCF of 546/499,7631/7697 is 13/3840803.

Greatest Common Factor of 546,7631

To find the highest common factor of 546,7631, we have to find the factors of both numbers and list the highest common factor.

The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546

The factors of 7631 are 1, 13, 587, 7631

The HCF of 546,7631 is 13.

Lets's calculate GCF of 546,7631

Greatest Common Factor (GCF) of 546,7631 By Common Division

13	546, 7631
	42, 587

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 546,7631 By Matching Biggest Common Factor Method

Now, list down the factors of 546

1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546

Now, list down the factors of 7631

1,13,587,7631

Greatest Common Factor

We found the factors 546,7631 . The biggest common factor number is the GCF number.
So the greatest common factor 546,7631 is 13.

Lets's calculate LCM of 499,7697

Lowest Common Multiple of 499,7697 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3840803

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/3840803

Therefore, the GCF of Fractions 546/499,7631/7697 is 13/3840803

Least Common Multiple of 499,7697 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 499,7697 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(499,7697) = 1

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

GCF(499,7697) x common factors =1 x 1 = 1

LCM(499,7697) = ( 499 × 7697 ) / 1

LCM(499,7697) = 3840803 / 1

LCM(499,7697) = 3840803

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FAQs on GCF of Fractions of 546/499, 7631/7697

1. What is the HCF of 546,7631?

The HCF of 546,7631 is 13

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 546/499, 7631/7697?

Answer: GCF of Numerators as per given numbers 546/499, 7631/7697 is

GCF of Numerators i.e. for 546,7631 is 13

LCM of denominators i.e. for 499,7697 is 3840803.

Thus, GCF of Fractions is 13/3840803.Finally, GCF of Fractions for 546/499, 7631/7697 is 13/3840803.