Greatest Common Factor of 21/45, 20/12, 68/86, 145/80

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 21/45, 20/12, 68/86, 145/80

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 21/45,20/12,68/86,145/80

Given fractions are 21/45,20/12,68/86,145/80

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 21,20,68,145

Greatest Common Factor of Numerators i.e. GCF of 21,20,68,145 is 1 .

LCM of Denominators means LCM of 45,12,86,80 as per the given fractions.

LCM of 45,12,86,80 is 30960 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 21,20,68,145

GCF of Fractions 21/45,20/12,68/86,145/80 is 1/30960

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

Greatest Common Factor of 21,20,68,145 By Matching Biggest Common Factor Method

Greatest Common Factor of 21,20,68,145 By Matching Biggest Common Factor Method

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

Factors of 145

List of positive integer factors of 145 that divides 145 without a remainder.

1,5,29,145

Greatest Common Factor

We found the factors 21,20,68,145 . The biggest common factor number is the GCF number.
So the greatest common factor 21,20,68,145 is 1.

Lets's calculate LCM of 45,12,86,80

2 45, 12, 86, 80
2 45, 6, 43, 40
3 45, 3, 43, 20
5 15, 1, 43, 20
3, 1, 43, 4

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 3 x 1 x 43 x 4 = 30960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30960

Therefore, the GCF of Fractions 21/45,20/12,68/86,145/80 is 1/30960

Least Common Multiple of 45,12,86,80 with GCF Formula

Least Common Multiple of 45,12,86,80 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 45,12,86,80 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,12,86,80) = 1

common factors(in case of two or more numbers have common factors) = 120

GCF(45,12,86,80) x common factors =1 x 120 = 120

LCM(45,12,86,80) = ( 45 × 12 × 86 × 80 ) / 120

LCM(45,12,86,80) = 3715200 / 120

LCM(45,12,86,80) = 30960


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 21/45, 20/12, 68/86, 145/80

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 21/45, 20/12, 68/86, 145/80?

Answer: GCF of Numerators as per given numbers 21/45, 20/12, 68/86, 145/80 is

GCF of Numerators i.e. for 21,20,68,145 is 1

LCM of denominators i.e. for 45,12,86,80 is 30960.

Thus, GCF of Fractions is 1/30960.Finally, GCF of Fractions for 21/45, 20/12, 68/86, 145/80 is 1/30960.