Greatest Common Factor of 67/54, 36/27, 10/75, 61/369

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 67/54, 36/27, 10/75, 61/369

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 67/54,36/27,10/75,61/369

Given fractions are 67/54,36/27,10/75,61/369

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 67,36,10,61

Greatest Common Factor of Numerators i.e. GCF of 67,36,10,61 is 1 .

LCM of Denominators means LCM of 54,27,75,369 as per the given fractions.

LCM of 54,27,75,369 is 55350 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 67,36,10,61

GCF of Fractions 67/54,36/27,10/75,61/369 is 1/55350

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

Greatest Common Factor of 67,36,10,61 By Matching Biggest Common Factor Method

Greatest Common Factor of 67,36,10,61 By Matching Biggest Common Factor Method

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1,61

Greatest Common Factor

We found the factors 67,36,10,61 . The biggest common factor number is the GCF number.
So the greatest common factor 67,36,10,61 is 1.

Lets's calculate LCM of 54,27,75,369

3 54, 27, 75, 369
3 18, 9, 25, 123
3 6, 3, 25, 41
2, 1, 25, 41

∴ So the LCM of the given numbers is 3 x 3 x 3 x 2 x 1 x 25 x 41 = 55350

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/55350

Therefore, the GCF of Fractions 67/54,36/27,10/75,61/369 is 1/55350

Least Common Multiple of 54,27,75,369 with GCF Formula

Least Common Multiple of 54,27,75,369 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 54,27,75,369 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,27,75,369) = 3

common factors(in case of two or more numbers have common factors) = 243

GCF(54,27,75,369) x common factors =3 x 243 = 729

LCM(54,27,75,369) = ( 54 × 27 × 75 × 369 ) / 729

LCM(54,27,75,369) = 40350150 / 729

LCM(54,27,75,369) = 55350


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 67/54, 36/27, 10/75, 61/369

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 67/54, 36/27, 10/75, 61/369?

Answer: GCF of Numerators as per given numbers 67/54, 36/27, 10/75, 61/369 is

GCF of Numerators i.e. for 67,36,10,61 is 1

LCM of denominators i.e. for 54,27,75,369 is 55350.

Thus, GCF of Fractions is 1/55350.Finally, GCF of Fractions for 67/54, 36/27, 10/75, 61/369 is 1/55350.