Greatest Common Factor of 414/60, 320/1970

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 414/60, 320/1970

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 414/60,320/1970

Given fractions are 414/60,320/1970

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 414,320

Greatest Common Factor of Numerators i.e. GCF of 414,320 is 2 .

LCM of Denominators means LCM of 60,1970 as per the given fractions.

LCM of 60,1970 is 11820 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 414,320

GCF of Fractions 414/60,320/1970 is 2/11820

2 414, 320
207, 160

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 414,320 By Matching Biggest Common Factor Method

Greatest Common Factor of 414,320 By Matching Biggest Common Factor Method

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Factors of 320

List of positive integer factors of 320 that divides 320 without a remainder.

1,2,4,5,8,10,16,20,32,40,64,80,160,320

Greatest Common Factor

We found the factors 414,320 . The biggest common factor number is the GCF number.
So the greatest common factor 414,320 is 2.

Lets's calculate LCM of 60,1970

2 60, 1970
5 30, 985
6, 197

∴ So the LCM of the given numbers is 2 x 5 x 6 x 197 = 11820

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11820

Therefore, the GCF of Fractions 414/60,320/1970 is 2/11820

Least Common Multiple of 60,1970 with GCF Formula

Least Common Multiple of 60,1970 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 60,1970 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(60,1970) = 10

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

GCF(60,1970) x common factors =10 x 1 = 10

LCM(60,1970) = ( 60 × 1970 ) / 10

LCM(60,1970) = 118200 / 10

LCM(60,1970) = 11820


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 414/60, 320/1970

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 414/60, 320/1970?

Answer: GCF of Numerators as per given numbers 414/60, 320/1970 is

GCF of Numerators i.e. for 414,320 is 2

LCM of denominators i.e. for 60,1970 is 11820.

Thus, GCF of Fractions is 2/11820.Finally, GCF of Fractions for 414/60, 320/1970 is 2/11820.