Greatest Common Factor of 3000/189, 7570/209

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 3000/189, 7570/209

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 3000/189,7570/209

Given fractions are 3000/189,7570/209

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 3000,7570

Greatest Common Factor of Numerators i.e. GCF of 3000,7570 is 10 .

LCM of Denominators means LCM of 189,209 as per the given fractions.

LCM of 189,209 is 39501 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 3000,7570

GCF of Fractions 3000/189,7570/209 is 10/39501

2 3000, 7570
5 1500, 3785
300, 757

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 3000,7570 By Matching Biggest Common Factor Method

Greatest Common Factor of 3000,7570 By Matching Biggest Common Factor Method

Factors of 3000

List of positive integer factors of 3000 that divides 3000 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,125,150,200,250,300,375,500,600,750,1000,1500,3000

Factors of 7570

List of positive integer factors of 7570 that divides 7570 without a remainder.

1,2,5,10,757,1514,3785,7570

Greatest Common Factor

We found the factors 3000,7570 . The biggest common factor number is the GCF number.
So the greatest common factor 3000,7570 is 10.

Lets's calculate LCM of 189,209

Given numbers has no common factors except 1. So, there LCM is their product i.e 39501

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/39501

Therefore, the GCF of Fractions 3000/189,7570/209 is 10/39501

Least Common Multiple of 189,209 with GCF Formula

Least Common Multiple of 189,209 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 189,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(189,209) = 1

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

GCF(189,209) x common factors =1 x 1 = 1

LCM(189,209) = ( 189 × 209 ) / 1

LCM(189,209) = 39501 / 1

LCM(189,209) = 39501


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 3000/189, 7570/209

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 3000/189, 7570/209?

Answer: GCF of Numerators as per given numbers 3000/189, 7570/209 is

GCF of Numerators i.e. for 3000,7570 is 10

LCM of denominators i.e. for 189,209 is 39501.

Thus, GCF of Fractions is 10/39501.Finally, GCF of Fractions for 3000/189, 7570/209 is 10/39501.