Greatest Common Factor of 38/31, 18/56, 75/49, 417/60

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 38/31, 18/56, 75/49, 417/60

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 38/31,18/56,75/49,417/60

Given fractions are 38/31,18/56,75/49,417/60

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 38,18,75,417

Greatest Common Factor of Numerators i.e. GCF of 38,18,75,417 is 1 .

LCM of Denominators means LCM of 31,56,49,60 as per the given fractions.

LCM of 31,56,49,60 is 182280 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 38,18,75,417

GCF of Fractions 38/31,18/56,75/49,417/60 is 1/182280

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

Greatest Common Factor of 38,18,75,417 By Matching Biggest Common Factor Method

Greatest Common Factor of 38,18,75,417 By Matching Biggest Common Factor Method

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 18

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

1,2,3,6,9,18

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1,3,139,417

Greatest Common Factor

We found the factors 38,18,75,417 . The biggest common factor number is the GCF number.
So the greatest common factor 38,18,75,417 is 1.

Lets's calculate LCM of 31,56,49,60

2 31, 56, 49, 60
2 31, 28, 49, 30
7 31, 14, 49, 15
31, 2, 7, 15

∴ So the LCM of the given numbers is 2 x 2 x 7 x 31 x 2 x 7 x 15 = 182280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/182280

Therefore, the GCF of Fractions 38/31,18/56,75/49,417/60 is 1/182280

Least Common Multiple of 31,56,49,60 with GCF Formula

Least Common Multiple of 31,56,49,60 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 31,56,49,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,56,49,60) = 1

common factors(in case of two or more numbers have common factors) = 28

GCF(31,56,49,60) x common factors =1 x 28 = 28

LCM(31,56,49,60) = ( 31 × 56 × 49 × 60 ) / 28

LCM(31,56,49,60) = 5103840 / 28

LCM(31,56,49,60) = 182280


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 38/31, 18/56, 75/49, 417/60

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 38/31, 18/56, 75/49, 417/60?

Answer: GCF of Numerators as per given numbers 38/31, 18/56, 75/49, 417/60 is

GCF of Numerators i.e. for 38,18,75,417 is 1

LCM of denominators i.e. for 31,56,49,60 is 182280.

Thus, GCF of Fractions is 1/182280.Finally, GCF of Fractions for 38/31, 18/56, 75/49, 417/60 is 1/182280.