Greatest Common Factor of 414/38, 507/42, 268/988

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 414/38, 507/42, 268/988

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 414/38,507/42,268/988

Given fractions are 414/38,507/42,268/988

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 414,507,268

Greatest Common Factor of Numerators i.e. GCF of 414,507,268 is 1 .

LCM of Denominators means LCM of 38,42,988 as per the given fractions.

LCM of 38,42,988 is 20748 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 414,507,268

GCF of Fractions 414/38,507/42,268/988 is 1/20748

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

Greatest Common Factor of 414,507,268 By Matching Biggest Common Factor Method

Greatest Common Factor of 414,507,268 By Matching Biggest Common Factor Method

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Factors of 507

List of positive integer factors of 507 that divides 507 without a remainder.

1,3,13,39,169,507

Factors of 268

List of positive integer factors of 268 that divides 268 without a remainder.

1,2,4,67,134,268

Greatest Common Factor

We found the factors 414,507,268 . The biggest common factor number is the GCF number.
So the greatest common factor 414,507,268 is 1.

Lets's calculate LCM of 38,42,988

2 38, 42, 988
19 19, 21, 494
1, 21, 26

∴ So the LCM of the given numbers is 2 x 19 x 1 x 21 x 26 = 20748

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20748

Therefore, the GCF of Fractions 414/38,507/42,268/988 is 1/20748

Least Common Multiple of 38,42,988 with GCF Formula

Least Common Multiple of 38,42,988 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 38,42,988 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,42,988) = 2

common factors(in case of two or more numbers have common factors) = 38

GCF(38,42,988) x common factors =2 x 38 = 76

LCM(38,42,988) = ( 38 × 42 × 988 ) / 76

LCM(38,42,988) = 1576848 / 76

LCM(38,42,988) = 20748


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 414/38, 507/42, 268/988

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 414/38, 507/42, 268/988?

Answer: GCF of Numerators as per given numbers 414/38, 507/42, 268/988 is

GCF of Numerators i.e. for 414,507,268 is 1

LCM of denominators i.e. for 38,42,988 is 20748.

Thus, GCF of Fractions is 1/20748.Finally, GCF of Fractions for 414/38, 507/42, 268/988 is 1/20748.