Greatest Common Factor of 65/84, 99/34, 25/84, 51/14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 65/84, 99/34, 25/84, 51/14

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 65/84,99/34,25/84,51/14

Given fractions are 65/84,99/34,25/84,51/14

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 65,99,25,51

Greatest Common Factor of Numerators i.e. GCF of 65,99,25,51 is 1 .

LCM of Denominators means LCM of 84,34,84,14 as per the given fractions.

LCM of 84,34,84,14 is 1428 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 65,99,25,51

GCF of Fractions 65/84,99/34,25/84,51/14 is 1/1428

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

Greatest Common Factor of 65,99,25,51 By Matching Biggest Common Factor Method

Greatest Common Factor of 65,99,25,51 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 99

List of positive integer factors of 99 that divides 99 without a remainder.

1,3,9,11,33,99

Factors of 25

List of positive integer factors of 25 that divides 25 without a remainder.

1,5,25

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1,3,17,51

Greatest Common Factor

We found the factors 65,99,25,51 . The biggest common factor number is the GCF number.
So the greatest common factor 65,99,25,51 is 1.

Lets's calculate LCM of 84,34,84,14

2 84, 34, 84, 14
2 42, 17, 42, 7
3 21, 17, 21, 7
7 7, 17, 7, 7
1, 17, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 17 x 1 x 1 = 1428

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1428

Therefore, the GCF of Fractions 65/84,99/34,25/84,51/14 is 1/1428

Least Common Multiple of 84,34,84,14 with GCF Formula

Least Common Multiple of 84,34,84,14 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 84,34,84,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,34,84,14) = 2

common factors(in case of two or more numbers have common factors) = 1176

GCF(84,34,84,14) x common factors =2 x 1176 = 2352

LCM(84,34,84,14) = ( 84 × 34 × 84 × 14 ) / 2352

LCM(84,34,84,14) = 3358656 / 2352

LCM(84,34,84,14) = 1428


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 65/84, 99/34, 25/84, 51/14

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 65/84, 99/34, 25/84, 51/14?

Answer: GCF of Numerators as per given numbers 65/84, 99/34, 25/84, 51/14 is

GCF of Numerators i.e. for 65,99,25,51 is 1

LCM of denominators i.e. for 84,34,84,14 is 1428.

Thus, GCF of Fractions is 1/1428.Finally, GCF of Fractions for 65/84, 99/34, 25/84, 51/14 is 1/1428.