Greatest Common Factor of 37/14, 17/75, 24/67, 25/108

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 37/14, 17/75, 24/67, 25/108

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 37/14,17/75,24/67,25/108

Given fractions are 37/14,17/75,24/67,25/108

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 37,17,24,25

Greatest Common Factor of Numerators i.e. GCF of 37,17,24,25 is 1 .

LCM of Denominators means LCM of 14,75,67,108 as per the given fractions.

LCM of 14,75,67,108 is 1266300 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 37,17,24,25

GCF of Fractions 37/14,17/75,24/67,25/108 is 1/1266300

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

Greatest Common Factor of 37,17,24,25 By Matching Biggest Common Factor Method

Greatest Common Factor of 37,17,24,25 By Matching Biggest Common Factor Method

Factors of 37

List of positive integer factors of 37 that divides 37 without a remainder.

1,37

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1,17

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1,2,3,4,6,8,12,24

Factors of 25

List of positive integer factors of 25 that divides 25 without a remainder.

1,5,25

Greatest Common Factor

We found the factors 37,17,24,25 . The biggest common factor number is the GCF number.
So the greatest common factor 37,17,24,25 is 1.

Lets's calculate LCM of 14,75,67,108

2 14, 75, 67, 108
3 7, 75, 67, 54
7, 25, 67, 18

∴ So the LCM of the given numbers is 2 x 3 x 7 x 25 x 67 x 18 = 1266300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1266300

Therefore, the GCF of Fractions 37/14,17/75,24/67,25/108 is 1/1266300

Least Common Multiple of 14,75,67,108 with GCF Formula

Least Common Multiple of 14,75,67,108 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 14,75,67,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,75,67,108) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(14,75,67,108) x common factors =1 x 6 = 6

LCM(14,75,67,108) = ( 14 × 75 × 67 × 108 ) / 6

LCM(14,75,67,108) = 7597800 / 6

LCM(14,75,67,108) = 1266300


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 37/14, 17/75, 24/67, 25/108

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 37/14, 17/75, 24/67, 25/108?

Answer: GCF of Numerators as per given numbers 37/14, 17/75, 24/67, 25/108 is

GCF of Numerators i.e. for 37,17,24,25 is 1

LCM of denominators i.e. for 14,75,67,108 is 1266300.

Thus, GCF of Fractions is 1/1266300.Finally, GCF of Fractions for 37/14, 17/75, 24/67, 25/108 is 1/1266300.