Greatest Common Factor of 65/212, 106/284

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 65/212, 106/284

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 65/212,106/284

Given fractions are 65/212,106/284

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 65,106

Greatest Common Factor of Numerators i.e. GCF of 65,106 is 1 .

LCM of Denominators means LCM of 212,284 as per the given fractions.

LCM of 212,284 is 15052 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 65,106

GCF of Fractions 65/212,106/284 is 1/15052

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

Greatest Common Factor of 65,106 By Matching Biggest Common Factor Method

Greatest Common Factor of 65,106 By Matching Biggest Common Factor Method

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1,5,13,65

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

Greatest Common Factor

We found the factors 65,106 . The biggest common factor number is the GCF number.
So the greatest common factor 65,106 is 1.

Lets's calculate LCM of 212,284

2 212, 284
2 106, 142
53, 71

∴ So the LCM of the given numbers is 2 x 2 x 53 x 71 = 15052

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15052

Therefore, the GCF of Fractions 65/212,106/284 is 1/15052

Least Common Multiple of 212,284 with GCF Formula

Least Common Multiple of 212,284 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 212,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(212,284) = 4

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

GCF(212,284) x common factors =4 x 1 = 4

LCM(212,284) = ( 212 × 284 ) / 4

LCM(212,284) = 60208 / 4

LCM(212,284) = 15052


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 65/212, 106/284

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 65/212, 106/284?

Answer: GCF of Numerators as per given numbers 65/212, 106/284 is

GCF of Numerators i.e. for 65,106 is 1

LCM of denominators i.e. for 212,284 is 15052.

Thus, GCF of Fractions is 1/15052.Finally, GCF of Fractions for 65/212, 106/284 is 1/15052.