Greatest Common Factor of 208/22, 768/312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 208/22, 768/312

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 208/22,768/312

Given fractions are 208/22,768/312

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 208,768

Greatest Common Factor of Numerators i.e. GCF of 208,768 is 16 .

LCM of Denominators means LCM of 22,312 as per the given fractions.

LCM of 22,312 is 3432 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 208,768

GCF of Fractions 208/22,768/312 is 16/3432

2 208, 768
2 104, 384
2 52, 192
2 26, 96
13, 48

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 208,768 By Matching Biggest Common Factor Method

Greatest Common Factor of 208,768 By Matching Biggest Common Factor Method

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1,2,4,8,13,16,26,52,104,208

Factors of 768

List of positive integer factors of 768 that divides 768 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Greatest Common Factor

We found the factors 208,768 . The biggest common factor number is the GCF number.
So the greatest common factor 208,768 is 16.

Lets's calculate LCM of 22,312

2 22, 312
11, 156

∴ So the LCM of the given numbers is 2 x 11 x 156 = 3432

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/3432

Therefore, the GCF of Fractions 208/22,768/312 is 16/3432

Least Common Multiple of 22,312 with GCF Formula

Least Common Multiple of 22,312 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 22,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,312) = 2

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

GCF(22,312) x common factors =2 x 1 = 2

LCM(22,312) = ( 22 × 312 ) / 2

LCM(22,312) = 6864 / 2

LCM(22,312) = 3432


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 208/22, 768/312

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 208/22, 768/312?

Answer: GCF of Numerators as per given numbers 208/22, 768/312 is

GCF of Numerators i.e. for 208,768 is 16

LCM of denominators i.e. for 22,312 is 3432.

Thus, GCF of Fractions is 16/3432.Finally, GCF of Fractions for 208/22, 768/312 is 16/3432.