Greatest Common Factor of 16/9, 82/4, 51/8, 65/4, 694/3, 17/4, 73/8, 854/6, 80/3, 32/6

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 16/9, 82/4, 51/8, 65/4, 694/3, 17/4, 73/8, 854/6, 80/3, 32/6

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 16/9,82/4,51/8,65/4,694/3,17/4,73/8,854/6,80/3,32/6

Given fractions are 16/9,82/4,51/8,65/4,694/3,17/4,73/8,854/6,80/3,32/6

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 16,82,51,65,694,17,73,854,80,32

Greatest Common Factor of Numerators i.e. GCF of 16,82,51,65,694,17,73,854,80,32 is 1 .

LCM of Denominators means LCM of 9,4,8,4,3,4,8,6,3,6 as per the given fractions.

LCM of 9,4,8,4,3,4,8,6,3,6 is 72 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 16,82,51,65,694,17,73,854,80,32

GCF of Fractions 16/9,82/4,51/8,65/4,694/3,17/4,73/8,854/6,80/3,32/6 is 1/72

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

Greatest Common Factor of 16,82,51,65,694,17,73,854,80,32 By Matching Biggest Common Factor Method

Greatest Common Factor of 16,82,51,65,694,17,73,854,80,32 By Matching Biggest Common Factor Method

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

Factors of 51

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

1,3,17,51

Factors of 65

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

1,5,13,65

Factors of 694

List of positive integer factors of 694 that divides 694 without a remainder.

1,2,347,694

Factors of 17

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

1,17

Factors of 73

List of positive integer factors of 73 that divides 73 without a remainder.

1,73

Factors of 854

List of positive integer factors of 854 that divides 854 without a remainder.

1,2,7,14,61,122,427,854

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1,2,4,5,8,10,16,20,40,80

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

Greatest Common Factor

We found the factors 16,82,51,65,694,17,73,854,80,32 . The biggest common factor number is the GCF number.
So the greatest common factor 16,82,51,65,694,17,73,854,80,32 is 1.

Lets's calculate LCM of 9,4,8,4,3,4,8,6,3,6

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

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 3 = 72

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72

Therefore, the GCF of Fractions 16/9,82/4,51/8,65/4,694/3,17/4,73/8,854/6,80/3,32/6 is 1/72

Least Common Multiple of 9,4,8,4,3,4,8,6,3,6 with GCF Formula

Least Common Multiple of 9,4,8,4,3,4,8,6,3,6 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 9,4,8,4,3,4,8,6,3,6 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(9,4,8,4,3,4,8,6,3,6) = 1

common factors(in case of two or more numbers have common factors) = 165888

GCF(9,4,8,4,3,4,8,6,3,6) x common factors =1 x 165888 = 165888

LCM(9,4,8,4,3,4,8,6,3,6) = ( 9 × 4 × 8 × 4 × 3 × 4 × 8 × 6 × 3 × 6 ) / 165888

LCM(9,4,8,4,3,4,8,6,3,6) = 11943936 / 165888

LCM(9,4,8,4,3,4,8,6,3,6) = 72


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 16/9, 82/4, 51/8, 65/4, 694/3, 17/4, 73/8, 854/6, 80/3, 32/6

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 16/9, 82/4, 51/8, 65/4, 694/3, 17/4, 73/8, 854/6, 80/3, 32/6?

Answer: GCF of Numerators as per given numbers 16/9, 82/4, 51/8, 65/4, 694/3, 17/4, 73/8, 854/6, 80/3, 32/6 is

GCF of Numerators i.e. for 16,82,51,65,694,17,73,854,80,32 is 1

LCM of denominators i.e. for 9,4,8,4,3,4,8,6,3,6 is 72.

Thus, GCF of Fractions is 1/72.Finally, GCF of Fractions for 16/9, 82/4, 51/8, 65/4, 694/3, 17/4, 73/8, 854/6, 80/3, 32/6 is 1/72.