Greatest Common Factor of 42/16, 75/65, 712/680

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 42/16, 75/65, 712/680

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 42/16,75/65,712/680

Given fractions are 42/16,75/65,712/680

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 42,75,712

Greatest Common Factor of Numerators i.e. GCF of 42,75,712 is 1 .

LCM of Denominators means LCM of 16,65,680 as per the given fractions.

LCM of 16,65,680 is 17680 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 42,75,712

GCF of Fractions 42/16,75/65,712/680 is 1/17680

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

Greatest Common Factor of 42,75,712 By Matching Biggest Common Factor Method

Greatest Common Factor of 42,75,712 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 75

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

1,3,5,15,25,75

Factors of 712

List of positive integer factors of 712 that divides 712 without a remainder.

1,2,4,8,89,178,356,712

Greatest Common Factor

We found the factors 42,75,712 . The biggest common factor number is the GCF number.
So the greatest common factor 42,75,712 is 1.

Lets's calculate LCM of 16,65,680

2 16, 65, 680
2 8, 65, 340
2 4, 65, 170
5 2, 65, 85
2, 13, 17

∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 2 x 13 x 17 = 17680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17680

Therefore, the GCF of Fractions 42/16,75/65,712/680 is 1/17680

Least Common Multiple of 16,65,680 with GCF Formula

Least Common Multiple of 16,65,680 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 16,65,680 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,65,680) = 1

common factors(in case of two or more numbers have common factors) = 40

GCF(16,65,680) x common factors =1 x 40 = 40

LCM(16,65,680) = ( 16 × 65 × 680 ) / 40

LCM(16,65,680) = 707200 / 40

LCM(16,65,680) = 17680


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 42/16, 75/65, 712/680

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 42/16, 75/65, 712/680?

Answer: GCF of Numerators as per given numbers 42/16, 75/65, 712/680 is

GCF of Numerators i.e. for 42,75,712 is 1

LCM of denominators i.e. for 16,65,680 is 17680.

Thus, GCF of Fractions is 1/17680.Finally, GCF of Fractions for 42/16, 75/65, 712/680 is 1/17680.