How to Find GCF of 23/80, 75/97, 123/165?

GCF of 23/80, 75/97, 123/165

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 23/80, 75/97, 123/165 i.e 1/256080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/80, 75/97, 123/165.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 23/80,75/97,123/165?

Given fractions are 23/80,75/97,123/165

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 23/80,75/97,123/165, numerators are 23,75,123

Denominators are 80,97,165

The GCF of 23,75,123 is 1 .

LCM of 80,97,165 is 256080.

The greatest common factor of 23/80,75/97,123/165 = [GCF of 23,75,123]/[LCM of 80,97,165]= 1/256080

Therefore, the GCF of 23/80,75/97,123/165 is 1/256080.

Greatest Common Factor of 23,75,123

To find the highest common factor of 23,75,123, we have to find the factors of both numbers and list the highest common factor.

The factors of 23 are 1, 23

The factors of 75 are 1, 3, 5, 15, 25, 75

The factors of 123 are 1, 3, 41, 123

The HCF of 23,75,123 is 1.

Lets's calculate GCF of 23,75,123

Greatest Common Factor (GCF) of 23,75,123 By Common Division

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

Greatest Common Factor of 23,75,123 By Matching Biggest Common Factor Method

Now, list down the factors of 23

1,23

Now, list down the factors of 75

1,3,5,15,25,75

Now, list down the factors of 123

1,3,41,123

Greatest Common Factor

We found the factors 23,75,123 . The biggest common factor number is the GCF number.
So the greatest common factor 23,75,123 is 1.

Lets's calculate LCM of 80,97,165

Lowest Common Multiple of 80,97,165 using Common Division

5	80, 97, 165
	16, 97, 33

∴ So the LCM of the given numbers is 5 x 16 x 97 x 33 = 256080

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/256080

Therefore, the GCF of Fractions 23/80,75/97,123/165 is 1/256080

Least Common Multiple of 80,97,165 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 80,97,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,97,165) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(80,97,165) x common factors =1 x 5 = 5

LCM(80,97,165) = ( 80 × 97 × 165 ) / 5

LCM(80,97,165) = 1280400 / 5

LCM(80,97,165) = 256080

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 23/80, 75/97, 123/165

1. What is the HCF of 23,75,123?

The HCF of 23,75,123 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 23/80, 75/97, 123/165?

Answer: GCF of Numerators as per given numbers 23/80, 75/97, 123/165 is

GCF of Numerators i.e. for 23,75,123 is 1

LCM of denominators i.e. for 80,97,165 is 256080.

Thus, GCF of Fractions is 1/256080.Finally, GCF of Fractions for 23/80, 75/97, 123/165 is 1/256080.