Greatest Common Factor of 65/14, 17/39, 828/49

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 65/14, 17/39, 828/49

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 65/14,17/39,828/49

Given fractions are 65/14,17/39,828/49

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 65,17,828

Greatest Common Factor of Numerators i.e. GCF of 65,17,828 is 1 .

LCM of Denominators means LCM of 14,39,49 as per the given fractions.

LCM of 14,39,49 is 3822 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 65,17,828

GCF of Fractions 65/14,17/39,828/49 is 1/3822

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

Greatest Common Factor of 65,17,828 By Matching Biggest Common Factor Method

Greatest Common Factor of 65,17,828 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 17

List of positive integer factors of 17 that divides 17 without a remainder.

1,17

Factors of 828

List of positive integer factors of 828 that divides 828 without a remainder.

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Greatest Common Factor

We found the factors 65,17,828 . The biggest common factor number is the GCF number.
So the greatest common factor 65,17,828 is 1.

Lets's calculate LCM of 14,39,49

7 14, 39, 49
2, 39, 7

∴ So the LCM of the given numbers is 7 x 2 x 39 x 7 = 3822

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3822

Therefore, the GCF of Fractions 65/14,17/39,828/49 is 1/3822

Least Common Multiple of 14,39,49 with GCF Formula

Least Common Multiple of 14,39,49 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 14,39,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,39,49) = 1

common factors(in case of two or more numbers have common factors) = 7

GCF(14,39,49) x common factors =1 x 7 = 7

LCM(14,39,49) = ( 14 × 39 × 49 ) / 7

LCM(14,39,49) = 26754 / 7

LCM(14,39,49) = 3822


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 65/14, 17/39, 828/49

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 65/14, 17/39, 828/49?

Answer: GCF of Numerators as per given numbers 65/14, 17/39, 828/49 is

GCF of Numerators i.e. for 65,17,828 is 1

LCM of denominators i.e. for 14,39,49 is 3822.

Thus, GCF of Fractions is 1/3822.Finally, GCF of Fractions for 65/14, 17/39, 828/49 is 1/3822.