Greatest Common Factor of 16/14, 39/42, 25/78, 82/39

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 16/14, 39/42, 25/78, 82/39

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 16/14,39/42,25/78,82/39

Given fractions are 16/14,39/42,25/78,82/39

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 16,39,25,82

Greatest Common Factor of Numerators i.e. GCF of 16,39,25,82 is 1 .

LCM of Denominators means LCM of 14,42,78,39 as per the given fractions.

LCM of 14,42,78,39 is 546 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 16,39,25,82

GCF of Fractions 16/14,39/42,25/78,82/39 is 1/546

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

Greatest Common Factor of 16,39,25,82 By Matching Biggest Common Factor Method

Greatest Common Factor of 16,39,25,82 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 39

List of positive integer factors of 39 that divides 39 without a remainder.

1,3,13,39

Factors of 25

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

1,5,25

Factors of 82

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

1,2,41,82

Greatest Common Factor

We found the factors 16,39,25,82 . The biggest common factor number is the GCF number.
So the greatest common factor 16,39,25,82 is 1.

Lets's calculate LCM of 14,42,78,39

2 14, 42, 78, 39
3 7, 21, 39, 39
7 7, 7, 13, 13
13 1, 1, 13, 13
1, 1, 1, 1

∴ So the LCM of the given numbers is 2 x 3 x 7 x 13 x 1 x 1 x 1 x 1 = 546

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/546

Therefore, the GCF of Fractions 16/14,39/42,25/78,82/39 is 1/546

Least Common Multiple of 14,42,78,39 with GCF Formula

Least Common Multiple of 14,42,78,39 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 14,42,78,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,42,78,39) = 1

common factors(in case of two or more numbers have common factors) = 3276

GCF(14,42,78,39) x common factors =1 x 3276 = 3276

LCM(14,42,78,39) = ( 14 × 42 × 78 × 39 ) / 3276

LCM(14,42,78,39) = 1788696 / 3276

LCM(14,42,78,39) = 546


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 16/14, 39/42, 25/78, 82/39

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 16/14, 39/42, 25/78, 82/39?

Answer: GCF of Numerators as per given numbers 16/14, 39/42, 25/78, 82/39 is

GCF of Numerators i.e. for 16,39,25,82 is 1

LCM of denominators i.e. for 14,42,78,39 is 546.

Thus, GCF of Fractions is 1/546.Finally, GCF of Fractions for 16/14, 39/42, 25/78, 82/39 is 1/546.