Greatest Common Factor of 85/78, 99/40, 58/42, 23/24

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 85/78, 99/40, 58/42, 23/24

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 85/78,99/40,58/42,23/24

Given fractions are 85/78,99/40,58/42,23/24

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 85,99,58,23

Greatest Common Factor of Numerators i.e. GCF of 85,99,58,23 is 1 .

LCM of Denominators means LCM of 78,40,42,24 as per the given fractions.

LCM of 78,40,42,24 is 10920 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 85,99,58,23

GCF of Fractions 85/78,99/40,58/42,23/24 is 1/10920

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

Greatest Common Factor of 85,99,58,23 By Matching Biggest Common Factor Method

Greatest Common Factor of 85,99,58,23 By Matching Biggest Common Factor Method

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1,5,17,85

Factors of 99

List of positive integer factors of 99 that divides 99 without a remainder.

1,3,9,11,33,99

Factors of 58

List of positive integer factors of 58 that divides 58 without a remainder.

1,2,29,58

Factors of 23

List of positive integer factors of 23 that divides 23 without a remainder.

1,23

Greatest Common Factor

We found the factors 85,99,58,23 . The biggest common factor number is the GCF number.
So the greatest common factor 85,99,58,23 is 1.

Lets's calculate LCM of 78,40,42,24

2 78, 40, 42, 24
2 39, 20, 21, 12
2 39, 10, 21, 6
3 39, 5, 21, 3
13, 5, 7, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 13 x 5 x 7 x 1 = 10920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10920

Therefore, the GCF of Fractions 85/78,99/40,58/42,23/24 is 1/10920

Least Common Multiple of 78,40,42,24 with GCF Formula

Least Common Multiple of 78,40,42,24 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 78,40,42,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,40,42,24) = 2

common factors(in case of two or more numbers have common factors) = 144

GCF(78,40,42,24) x common factors =2 x 144 = 288

LCM(78,40,42,24) = ( 78 × 40 × 42 × 24 ) / 288

LCM(78,40,42,24) = 3144960 / 288

LCM(78,40,42,24) = 10920


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 85/78, 99/40, 58/42, 23/24

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 85/78, 99/40, 58/42, 23/24?

Answer: GCF of Numerators as per given numbers 85/78, 99/40, 58/42, 23/24 is

GCF of Numerators i.e. for 85,99,58,23 is 1

LCM of denominators i.e. for 78,40,42,24 is 10920.

Thus, GCF of Fractions is 1/10920.Finally, GCF of Fractions for 85/78, 99/40, 58/42, 23/24 is 1/10920.