Greatest Common Factor of 51/19, 12/76, 77/16, 18/14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 51/19, 12/76, 77/16, 18/14

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 51/19,12/76,77/16,18/14

Given fractions are 51/19,12/76,77/16,18/14

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 51,12,77,18

Greatest Common Factor of Numerators i.e. GCF of 51,12,77,18 is 1 .

LCM of Denominators means LCM of 19,76,16,14 as per the given fractions.

LCM of 19,76,16,14 is 2128 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 51,12,77,18

GCF of Fractions 51/19,12/76,77/16,18/14 is 1/2128

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

Greatest Common Factor of 51,12,77,18 By Matching Biggest Common Factor Method

Greatest Common Factor of 51,12,77,18 By Matching Biggest Common Factor Method

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1,3,17,51

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 77

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

1,7,11,77

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1,2,3,6,9,18

Greatest Common Factor

We found the factors 51,12,77,18 . The biggest common factor number is the GCF number.
So the greatest common factor 51,12,77,18 is 1.

Lets's calculate LCM of 19,76,16,14

2 19, 76, 16, 14
2 19, 38, 8, 7
19 19, 19, 4, 7
1, 1, 4, 7

∴ So the LCM of the given numbers is 2 x 2 x 19 x 1 x 1 x 4 x 7 = 2128

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2128

Therefore, the GCF of Fractions 51/19,12/76,77/16,18/14 is 1/2128

Least Common Multiple of 19,76,16,14 with GCF Formula

Least Common Multiple of 19,76,16,14 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 19,76,16,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(19,76,16,14) = 1

common factors(in case of two or more numbers have common factors) = 152

GCF(19,76,16,14) x common factors =1 x 152 = 152

LCM(19,76,16,14) = ( 19 × 76 × 16 × 14 ) / 152

LCM(19,76,16,14) = 323456 / 152

LCM(19,76,16,14) = 2128


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 51/19, 12/76, 77/16, 18/14

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 51/19, 12/76, 77/16, 18/14?

Answer: GCF of Numerators as per given numbers 51/19, 12/76, 77/16, 18/14 is

GCF of Numerators i.e. for 51,12,77,18 is 1

LCM of denominators i.e. for 19,76,16,14 is 2128.

Thus, GCF of Fractions is 1/2128.Finally, GCF of Fractions for 51/19, 12/76, 77/16, 18/14 is 1/2128.