Greatest Common Factor of 39/20, 85/84, 213/175

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 39/20, 85/84, 213/175

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 39/20,85/84,213/175

Given fractions are 39/20,85/84,213/175

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 39,85,213

Greatest Common Factor of Numerators i.e. GCF of 39,85,213 is 1 .

LCM of Denominators means LCM of 20,84,175 as per the given fractions.

LCM of 20,84,175 is 2100 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 39,85,213

GCF of Fractions 39/20,85/84,213/175 is 1/2100

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

Greatest Common Factor of 39,85,213 By Matching Biggest Common Factor Method

Greatest Common Factor of 39,85,213 By Matching Biggest Common Factor Method

Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1,3,13,39

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1,5,17,85

Factors of 213

List of positive integer factors of 213 that divides 213 without a remainder.

1,3,71,213

Greatest Common Factor

We found the factors 39,85,213 . The biggest common factor number is the GCF number.
So the greatest common factor 39,85,213 is 1.

Lets's calculate LCM of 20,84,175

2 20, 84, 175
2 10, 42, 175
5 5, 21, 175
7 1, 21, 35
1, 3, 5

∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 1 x 3 x 5 = 2100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2100

Therefore, the GCF of Fractions 39/20,85/84,213/175 is 1/2100

Least Common Multiple of 20,84,175 with GCF Formula

Least Common Multiple of 20,84,175 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 20,84,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,84,175) = 1

common factors(in case of two or more numbers have common factors) = 140

GCF(20,84,175) x common factors =1 x 140 = 140

LCM(20,84,175) = ( 20 × 84 × 175 ) / 140

LCM(20,84,175) = 294000 / 140

LCM(20,84,175) = 2100


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 39/20, 85/84, 213/175

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 39/20, 85/84, 213/175?

Answer: GCF of Numerators as per given numbers 39/20, 85/84, 213/175 is

GCF of Numerators i.e. for 39,85,213 is 1

LCM of denominators i.e. for 20,84,175 is 2100.

Thus, GCF of Fractions is 1/2100.Finally, GCF of Fractions for 39/20, 85/84, 213/175 is 1/2100.