Greatest Common Factor of 10/45, 27/22, 38/12, 161/18

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 10/45, 27/22, 38/12, 161/18

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 10/45,27/22,38/12,161/18

Given fractions are 10/45,27/22,38/12,161/18

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 10,27,38,161

Greatest Common Factor of Numerators i.e. GCF of 10,27,38,161 is 1 .

LCM of Denominators means LCM of 45,22,12,18 as per the given fractions.

LCM of 45,22,12,18 is 1980 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 10,27,38,161

GCF of Fractions 10/45,27/22,38/12,161/18 is 1/1980

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

Greatest Common Factor of 10,27,38,161 By Matching Biggest Common Factor Method

Greatest Common Factor of 10,27,38,161 By Matching Biggest Common Factor Method

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1,3,9,27

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 161

List of positive integer factors of 161 that divides 161 without a remainder.

1,7,23,161

Greatest Common Factor

We found the factors 10,27,38,161 . The biggest common factor number is the GCF number.
So the greatest common factor 10,27,38,161 is 1.

Lets's calculate LCM of 45,22,12,18

2 45, 22, 12, 18
3 45, 11, 6, 9
3 15, 11, 2, 3
5, 11, 2, 1

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 11 x 2 x 1 = 1980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1980

Therefore, the GCF of Fractions 10/45,27/22,38/12,161/18 is 1/1980

Least Common Multiple of 45,22,12,18 with GCF Formula

Least Common Multiple of 45,22,12,18 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 45,22,12,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,22,12,18) = 1

common factors(in case of two or more numbers have common factors) = 108

GCF(45,22,12,18) x common factors =1 x 108 = 108

LCM(45,22,12,18) = ( 45 × 22 × 12 × 18 ) / 108

LCM(45,22,12,18) = 213840 / 108

LCM(45,22,12,18) = 1980


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 10/45, 27/22, 38/12, 161/18

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 10/45, 27/22, 38/12, 161/18?

Answer: GCF of Numerators as per given numbers 10/45, 27/22, 38/12, 161/18 is

GCF of Numerators i.e. for 10,27,38,161 is 1

LCM of denominators i.e. for 45,22,12,18 is 1980.

Thus, GCF of Fractions is 1/1980.Finally, GCF of Fractions for 10/45, 27/22, 38/12, 161/18 is 1/1980.