How to Find GCF of 2977/580, 3675/3484?

GCF of 2977/580, 3675/3484

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 2977/580, 3675/3484 i.e 1/505180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2977/580, 3675/3484.

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 2977/580,3675/3484?

Given fractions are 2977/580,3675/3484

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 2977/580,3675/3484, numerators are 2977,3675

Denominators are 580,3484

The GCF of 2977,3675 is 1 .

LCM of 580,3484 is 505180.

The greatest common factor of 2977/580,3675/3484 = [GCF of 2977,3675]/[LCM of 580,3484]= 1/505180

Therefore, the GCF of 2977/580,3675/3484 is 1/505180.

Greatest Common Factor of 2977,3675

To find the highest common factor of 2977,3675, we have to find the factors of both numbers and list the highest common factor.

The factors of 2977 are 1, 13, 229, 2977

The factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675

The HCF of 2977,3675 is 1.

Lets's calculate GCF of 2977,3675

Greatest Common Factor (GCF) of 2977,3675 By Common Division

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

Greatest Common Factor of 2977,3675 By Matching Biggest Common Factor Method

Now, list down the factors of 2977

1,13,229,2977

Now, list down the factors of 3675

1,3,5,7,15,21,25,35,49,75,105,147,175,245,525,735,1225,3675

Greatest Common Factor

We found the factors 2977,3675 . The biggest common factor number is the GCF number.
So the greatest common factor 2977,3675 is 1.

Lets's calculate LCM of 580,3484

Lowest Common Multiple of 580,3484 using Common Division

2	580, 3484
2	290, 1742
	145, 871

∴ So the LCM of the given numbers is 2 x 2 x 145 x 871 = 505180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/505180

Therefore, the GCF of Fractions 2977/580,3675/3484 is 1/505180

Least Common Multiple of 580,3484 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 580,3484 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(580,3484) = 4

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

GCF(580,3484) x common factors =4 x 1 = 4

LCM(580,3484) = ( 580 × 3484 ) / 4

LCM(580,3484) = 2020720 / 4

LCM(580,3484) = 505180

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FAQs on GCF of Fractions of 2977/580, 3675/3484

1. What is the HCF of 2977,3675?

The HCF of 2977,3675 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 2977/580, 3675/3484?

Answer: GCF of Numerators as per given numbers 2977/580, 3675/3484 is

GCF of Numerators i.e. for 2977,3675 is 1

LCM of denominators i.e. for 580,3484 is 505180.

Thus, GCF of Fractions is 1/505180.Finally, GCF of Fractions for 2977/580, 3675/3484 is 1/505180.