How to Find GCF of 3977/468, 1993/9564?

GCF of 3977/468, 1993/9564

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 3977/468, 1993/9564 i.e 1/372996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3977/468, 1993/9564.

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 3977/468,1993/9564?

Given fractions are 3977/468,1993/9564

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 3977/468,1993/9564, numerators are 3977,1993

Denominators are 468,9564

The GCF of 3977,1993 is 1 .

LCM of 468,9564 is 372996.

The greatest common factor of 3977/468,1993/9564 = [GCF of 3977,1993]/[LCM of 468,9564]= 1/372996

Therefore, the GCF of 3977/468,1993/9564 is 1/372996.

Greatest Common Factor of 3977,1993

To find the highest common factor of 3977,1993, we have to find the factors of both numbers and list the highest common factor.

The factors of 3977 are 1, 41, 97, 3977

The factors of 1993 are 1, 1993

The HCF of 3977,1993 is 1.

Lets's calculate GCF of 3977,1993

Greatest Common Factor (GCF) of 3977,1993 By Common Division

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

Greatest Common Factor of 3977,1993 By Matching Biggest Common Factor Method

Now, list down the factors of 3977

1,41,97,3977

Now, list down the factors of 1993

1,1993

Greatest Common Factor

We found the factors 3977,1993 . The biggest common factor number is the GCF number.
So the greatest common factor 3977,1993 is 1.

Lets's calculate LCM of 468,9564

Lowest Common Multiple of 468,9564 using Common Division

2	468, 9564
2	234, 4782
3	117, 2391
	39, 797

∴ So the LCM of the given numbers is 2 x 2 x 3 x 39 x 797 = 372996

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/372996

Therefore, the GCF of Fractions 3977/468,1993/9564 is 1/372996

Least Common Multiple of 468,9564 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 468,9564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(468,9564) = 12

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

GCF(468,9564) x common factors =12 x 1 = 12

LCM(468,9564) = ( 468 × 9564 ) / 12

LCM(468,9564) = 4475952 / 12

LCM(468,9564) = 372996

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FAQs on GCF of Fractions of 3977/468, 1993/9564

1. What is the HCF of 3977,1993?

The HCF of 3977,1993 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 3977/468, 1993/9564?

Answer: GCF of Numerators as per given numbers 3977/468, 1993/9564 is

GCF of Numerators i.e. for 3977,1993 is 1

LCM of denominators i.e. for 468,9564 is 372996.

Thus, GCF of Fractions is 1/372996.Finally, GCF of Fractions for 3977/468, 1993/9564 is 1/372996.