Greatest Common Factor of 42/49, 16/84, 772/12

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 42/49, 16/84, 772/12

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 42/49,16/84,772/12

Given fractions are 42/49,16/84,772/12

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 42,16,772

Greatest Common Factor of Numerators i.e. GCF of 42,16,772 is 2 .

LCM of Denominators means LCM of 49,84,12 as per the given fractions.

LCM of 49,84,12 is 588 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 42,16,772

GCF of Fractions 42/49,16/84,772/12 is 2/588

2 42, 16, 772
21, 8, 386

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 42,16,772 By Matching Biggest Common Factor Method

Greatest Common Factor of 42,16,772 By Matching Biggest Common Factor Method

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Factors of 772

List of positive integer factors of 772 that divides 772 without a remainder.

1,2,4,193,386,772

Greatest Common Factor

We found the factors 42,16,772 . The biggest common factor number is the GCF number.
So the greatest common factor 42,16,772 is 2.

Lets's calculate LCM of 49,84,12

2 49, 84, 12
2 49, 42, 6
3 49, 21, 3
7 49, 7, 1
1, 7, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 7 x 1 = 588

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/588

Therefore, the GCF of Fractions 42/49,16/84,772/12 is 2/588

Least Common Multiple of 49,84,12 with GCF Formula

Least Common Multiple of 49,84,12 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 49,84,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(49,84,12) = 1

common factors(in case of two or more numbers have common factors) = 84

GCF(49,84,12) x common factors =1 x 84 = 84

LCM(49,84,12) = ( 49 × 84 × 12 ) / 84

LCM(49,84,12) = 49392 / 84

LCM(49,84,12) = 588


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 42/49, 16/84, 772/12

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 42/49, 16/84, 772/12?

Answer: GCF of Numerators as per given numbers 42/49, 16/84, 772/12 is

GCF of Numerators i.e. for 42,16,772 is 2

LCM of denominators i.e. for 49,84,12 is 588.

Thus, GCF of Fractions is 2/588.Finally, GCF of Fractions for 42/49, 16/84, 772/12 is 2/588.