Greatest Common Factor of 77/52, 20/16, 204/16

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 77/52, 20/16, 204/16

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 77/52,20/16,204/16

Given fractions are 77/52,20/16,204/16

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 77,20,204

Greatest Common Factor of Numerators i.e. GCF of 77,20,204 is 1 .

LCM of Denominators means LCM of 52,16,16 as per the given fractions.

LCM of 52,16,16 is 208 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 77,20,204

GCF of Fractions 77/52,20/16,204/16 is 1/208

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

Greatest Common Factor of 77,20,204 By Matching Biggest Common Factor Method

Greatest Common Factor of 77,20,204 By Matching Biggest Common Factor Method

Factors of 77

List of positive integer factors of 77 that divides 77 without a remainder.

1,7,11,77

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

1,2,3,4,6,12,17,34,51,68,102,204

Greatest Common Factor

We found the factors 77,20,204 . The biggest common factor number is the GCF number.
So the greatest common factor 77,20,204 is 1.

Lets's calculate LCM of 52,16,16

2 52, 16, 16
2 26, 8, 8
2 13, 4, 4
2 13, 2, 2
13, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 13 x 1 x 1 = 208

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/208

Therefore, the GCF of Fractions 77/52,20/16,204/16 is 1/208

Least Common Multiple of 52,16,16 with GCF Formula

Least Common Multiple of 52,16,16 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 52,16,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,16,16) = 4

common factors(in case of two or more numbers have common factors) = 16

GCF(52,16,16) x common factors =4 x 16 = 64

LCM(52,16,16) = ( 52 × 16 × 16 ) / 64

LCM(52,16,16) = 13312 / 64

LCM(52,16,16) = 208


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 77/52, 20/16, 204/16

1. 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.

2. What is the GCF of Fractions for 77/52, 20/16, 204/16?

Answer: GCF of Numerators as per given numbers 77/52, 20/16, 204/16 is

GCF of Numerators i.e. for 77,20,204 is 1

LCM of denominators i.e. for 52,16,16 is 208.

Thus, GCF of Fractions is 1/208.Finally, GCF of Fractions for 77/52, 20/16, 204/16 is 1/208.