Greatest Common Factor of 51/8, 21/1, 71/8, 51/5, 126/6, 65/9, 17/2, 832/1, 86/1, 79/8

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 51/8, 21/1, 71/8, 51/5, 126/6, 65/9, 17/2, 832/1, 86/1, 79/8

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 51/8,21/1,71/8,51/5,126/6,65/9,17/2,832/1,86/1,79/8

Given fractions are 51/8,21/1,71/8,51/5,126/6,65/9,17/2,832/1,86/1,79/8

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 51,21,71,51,126,65,17,832,86,79

Greatest Common Factor of Numerators i.e. GCF of 51,21,71,51,126,65,17,832,86,79 is 1 .

LCM of Denominators means LCM of 8,1,8,5,6,9,2,1,1,8 as per the given fractions.

LCM of 8,1,8,5,6,9,2,1,1,8 is 360 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 51,21,71,51,126,65,17,832,86,79

GCF of Fractions 51/8,21/1,71/8,51/5,126/6,65/9,17/2,832/1,86/1,79/8 is 1/360

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

Greatest Common Factor of 51,21,71,51,126,65,17,832,86,79 By Matching Biggest Common Factor Method

Greatest Common Factor of 51,21,71,51,126,65,17,832,86,79 By Matching Biggest Common Factor Method

Factors of 51

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

1,3,17,51

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Factors of 71

List of positive integer factors of 71 that divides 71 without a remainder.

1,71

Factors of 51

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

1,3,17,51

Factors of 126

List of positive integer factors of 126 that divides 126 without a remainder.

1,2,3,6,7,9,14,18,21,42,63,126

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 832

List of positive integer factors of 832 that divides 832 without a remainder.

1,2,4,8,13,16,26,32,52,64,104,208,416,832

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1,2,43,86

Factors of 79

List of positive integer factors of 79 that divides 79 without a remainder.

1,79

Greatest Common Factor

We found the factors 51,21,71,51,126,65,17,832,86,79 . The biggest common factor number is the GCF number.
So the greatest common factor 51,21,71,51,126,65,17,832,86,79 is 1.

Lets's calculate LCM of 8,1,8,5,6,9,2,1,1,8

2 8, 1, 8, 5, 6, 9, 2, 1, 1, 8
2 4, 1, 4, 5, 3, 9, 1, 1, 1, 4
2 2, 1, 2, 5, 3, 9, 1, 1, 1, 2
3 1, 1, 1, 5, 3, 9, 1, 1, 1, 1
1, 1, 1, 5, 1, 3, 1, 1, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 1 x 5 x 1 x 3 x 1 x 1 x 1 x 1 = 360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/360

Therefore, the GCF of Fractions 51/8,21/1,71/8,51/5,126/6,65/9,17/2,832/1,86/1,79/8 is 1/360

Least Common Multiple of 8,1,8,5,6,9,2,1,1,8 with GCF Formula

Least Common Multiple of 8,1,8,5,6,9,2,1,1,8 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 8,1,8,5,6,9,2,1,1,8 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(8,1,8,5,6,9,2,1,1,8) = 1

common factors(in case of two or more numbers have common factors) = 768

GCF(8,1,8,5,6,9,2,1,1,8) x common factors =1 x 768 = 768

LCM(8,1,8,5,6,9,2,1,1,8) = ( 8 × 1 × 8 × 5 × 6 × 9 × 2 × 1 × 1 × 8 ) / 768

LCM(8,1,8,5,6,9,2,1,1,8) = 276480 / 768

LCM(8,1,8,5,6,9,2,1,1,8) = 360


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 51/8, 21/1, 71/8, 51/5, 126/6, 65/9, 17/2, 832/1, 86/1, 79/8

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 51/8, 21/1, 71/8, 51/5, 126/6, 65/9, 17/2, 832/1, 86/1, 79/8?

Answer: GCF of Numerators as per given numbers 51/8, 21/1, 71/8, 51/5, 126/6, 65/9, 17/2, 832/1, 86/1, 79/8 is

GCF of Numerators i.e. for 51,21,71,51,126,65,17,832,86,79 is 1

LCM of denominators i.e. for 8,1,8,5,6,9,2,1,1,8 is 360.

Thus, GCF of Fractions is 1/360.Finally, GCF of Fractions for 51/8, 21/1, 71/8, 51/5, 126/6, 65/9, 17/2, 832/1, 86/1, 79/8 is 1/360.