How to Find GCF of 3739/320, 1971/3164?

GCF of 3739/320, 1971/3164

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 3739/320, 1971/3164 i.e 1/253120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3739/320, 1971/3164.

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 3739/320,1971/3164?

Given fractions are 3739/320,1971/3164

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 3739/320,1971/3164, numerators are 3739,1971

Denominators are 320,3164

The GCF of 3739,1971 is 1 .

LCM of 320,3164 is 253120.

The greatest common factor of 3739/320,1971/3164 = [GCF of 3739,1971]/[LCM of 320,3164]= 1/253120

Therefore, the GCF of 3739/320,1971/3164 is 1/253120.

Greatest Common Factor of 3739,1971

To find the highest common factor of 3739,1971, we have to find the factors of both numbers and list the highest common factor.

The factors of 3739 are 1, 3739

The factors of 1971 are 1, 3, 9, 27, 73, 219, 657, 1971

The HCF of 3739,1971 is 1.

Lets's calculate GCF of 3739,1971

Greatest Common Factor (GCF) of 3739,1971 By Common Division

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

Greatest Common Factor of 3739,1971 By Matching Biggest Common Factor Method

Now, list down the factors of 3739

1,3739

Now, list down the factors of 1971

1,3,9,27,73,219,657,1971

Greatest Common Factor

We found the factors 3739,1971 . The biggest common factor number is the GCF number.
So the greatest common factor 3739,1971 is 1.

Lets's calculate LCM of 320,3164

Lowest Common Multiple of 320,3164 using Common Division

2	320, 3164
2	160, 1582
	80, 791

∴ So the LCM of the given numbers is 2 x 2 x 80 x 791 = 253120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/253120

Therefore, the GCF of Fractions 3739/320,1971/3164 is 1/253120

Least Common Multiple of 320,3164 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 320,3164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(320,3164) = 4

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

GCF(320,3164) x common factors =4 x 1 = 4

LCM(320,3164) = ( 320 × 3164 ) / 4

LCM(320,3164) = 1012480 / 4

LCM(320,3164) = 253120

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FAQs on GCF of Fractions of 3739/320, 1971/3164

1. What is the HCF of 3739,1971?

The HCF of 3739,1971 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 3739/320, 1971/3164?

Answer: GCF of Numerators as per given numbers 3739/320, 1971/3164 is

GCF of Numerators i.e. for 3739,1971 is 1

LCM of denominators i.e. for 320,3164 is 253120.

Thus, GCF of Fractions is 1/253120.Finally, GCF of Fractions for 3739/320, 1971/3164 is 1/253120.