Greatest Common Factor of 53/13, 78/24, 16/36, 75/68

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 53/13, 78/24, 16/36, 75/68

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 53/13,78/24,16/36,75/68

Given fractions are 53/13,78/24,16/36,75/68

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 53,78,16,75

Greatest Common Factor of Numerators i.e. GCF of 53,78,16,75 is 1 .

LCM of Denominators means LCM of 13,24,36,68 as per the given fractions.

LCM of 13,24,36,68 is 15912 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 53,78,16,75

GCF of Fractions 53/13,78/24,16/36,75/68 is 1/15912

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

Greatest Common Factor of 53,78,16,75 By Matching Biggest Common Factor Method

Greatest Common Factor of 53,78,16,75 By Matching Biggest Common Factor Method

Factors of 53

List of positive integer factors of 53 that divides 53 without a remainder.

1,53

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Factors of 16

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

1,2,4,8,16

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Greatest Common Factor

We found the factors 53,78,16,75 . The biggest common factor number is the GCF number.
So the greatest common factor 53,78,16,75 is 1.

Lets's calculate LCM of 13,24,36,68

2 13, 24, 36, 68
2 13, 12, 18, 34
3 13, 6, 9, 17
13, 2, 3, 17

∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 2 x 3 x 17 = 15912

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15912

Therefore, the GCF of Fractions 53/13,78/24,16/36,75/68 is 1/15912

Least Common Multiple of 13,24,36,68 with GCF Formula

Least Common Multiple of 13,24,36,68 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 13,24,36,68 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,24,36,68) = 1

common factors(in case of two or more numbers have common factors) = 48

GCF(13,24,36,68) x common factors =1 x 48 = 48

LCM(13,24,36,68) = ( 13 × 24 × 36 × 68 ) / 48

LCM(13,24,36,68) = 763776 / 48

LCM(13,24,36,68) = 15912


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 53/13, 78/24, 16/36, 75/68

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 53/13, 78/24, 16/36, 75/68?

Answer: GCF of Numerators as per given numbers 53/13, 78/24, 16/36, 75/68 is

GCF of Numerators i.e. for 53,78,16,75 is 1

LCM of denominators i.e. for 13,24,36,68 is 15912.

Thus, GCF of Fractions is 1/15912.Finally, GCF of Fractions for 53/13, 78/24, 16/36, 75/68 is 1/15912.