Greatest Common Factor of 456/17, 180/120

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 456/17, 180/120

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 456/17,180/120

Given fractions are 456/17,180/120

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 456,180

Greatest Common Factor of Numerators i.e. GCF of 456,180 is 12 .

LCM of Denominators means LCM of 17,120 as per the given fractions.

LCM of 17,120 is 2040 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 456,180

GCF of Fractions 456/17,180/120 is 12/2040

2 456, 180
2 228, 90
3 114, 45
38, 15

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 456,180 By Matching Biggest Common Factor Method

Greatest Common Factor of 456,180 By Matching Biggest Common Factor Method

Factors of 456

List of positive integer factors of 456 that divides 456 without a remainder.

1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Greatest Common Factor

We found the factors 456,180 . The biggest common factor number is the GCF number.
So the greatest common factor 456,180 is 12.

Lets's calculate LCM of 17,120

Given numbers has no common factors except 1. So, there LCM is their product i.e 2040

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/2040

Therefore, the GCF of Fractions 456/17,180/120 is 12/2040

Least Common Multiple of 17,120 with GCF Formula

Least Common Multiple of 17,120 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 17,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,120) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(17,120) x common factors =1 x 1 = 1

LCM(17,120) = ( 17 × 120 ) / 1

LCM(17,120) = 2040 / 1

LCM(17,120) = 2040


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 456/17, 180/120

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 456/17, 180/120?

Answer: GCF of Numerators as per given numbers 456/17, 180/120 is

GCF of Numerators i.e. for 456,180 is 12

LCM of denominators i.e. for 17,120 is 2040.

Thus, GCF of Fractions is 12/2040.Finally, GCF of Fractions for 456/17, 180/120 is 12/2040.