Greatest Common Factor of 89/68, 82/75, 60/42, 178/28

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 89/68, 82/75, 60/42, 178/28

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 89/68,82/75,60/42,178/28

Given fractions are 89/68,82/75,60/42,178/28

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 89,82,60,178

Greatest Common Factor of Numerators i.e. GCF of 89,82,60,178 is 1 .

LCM of Denominators means LCM of 68,75,42,28 as per the given fractions.

LCM of 68,75,42,28 is 35700 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 89,82,60,178

GCF of Fractions 89/68,82/75,60/42,178/28 is 1/35700

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

Greatest Common Factor of 89,82,60,178 By Matching Biggest Common Factor Method

Greatest Common Factor of 89,82,60,178 By Matching Biggest Common Factor Method

Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

1,89

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

Factors of 178

List of positive integer factors of 178 that divides 178 without a remainder.

1,2,89,178

Greatest Common Factor

We found the factors 89,82,60,178 . The biggest common factor number is the GCF number.
So the greatest common factor 89,82,60,178 is 1.

Lets's calculate LCM of 68,75,42,28

2 68, 75, 42, 28
2 34, 75, 21, 14
3 17, 75, 21, 7
7 17, 25, 7, 7
17, 25, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 17 x 25 x 1 x 1 = 35700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35700

Therefore, the GCF of Fractions 89/68,82/75,60/42,178/28 is 1/35700

Least Common Multiple of 68,75,42,28 with GCF Formula

Least Common Multiple of 68,75,42,28 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 68,75,42,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,75,42,28) = 1

common factors(in case of two or more numbers have common factors) = 168

GCF(68,75,42,28) x common factors =1 x 168 = 168

LCM(68,75,42,28) = ( 68 × 75 × 42 × 28 ) / 168

LCM(68,75,42,28) = 5997600 / 168

LCM(68,75,42,28) = 35700


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 89/68, 82/75, 60/42, 178/28

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 89/68, 82/75, 60/42, 178/28?

Answer: GCF of Numerators as per given numbers 89/68, 82/75, 60/42, 178/28 is

GCF of Numerators i.e. for 89,82,60,178 is 1

LCM of denominators i.e. for 68,75,42,28 is 35700.

Thus, GCF of Fractions is 1/35700.Finally, GCF of Fractions for 89/68, 82/75, 60/42, 178/28 is 1/35700.