Greatest Common Factor of 105/36, 150/54, 210/126

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 105/36, 150/54, 210/126

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 105/36,150/54,210/126

Given fractions are 105/36,150/54,210/126

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 105,150,210

Greatest Common Factor of Numerators i.e. GCF of 105,150,210 is 15 .

LCM of Denominators means LCM of 36,54,126 as per the given fractions.

LCM of 36,54,126 is 756 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 105,150,210

GCF of Fractions 105/36,150/54,210/126 is 15/756

3 105, 150, 210
5 35, 50, 70
7, 10, 14

∴ So the GCF of the given numbers is 3 x 5 = 15

Greatest Common Factor of 105,150,210 By Matching Biggest Common Factor Method

Greatest Common Factor of 105,150,210 By Matching Biggest Common Factor Method

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

Factors of 150

List of positive integer factors of 150 that divides 150 without a remainder.

1,2,3,5,6,10,15,25,30,50,75,150

Factors of 210

List of positive integer factors of 210 that divides 210 without a remainder.

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 105,150,210 . The biggest common factor number is the GCF number.
So the greatest common factor 105,150,210 is 15.

Lets's calculate LCM of 36,54,126

2 36, 54, 126
3 18, 27, 63
3 6, 9, 21
2, 3, 7

∴ So the LCM of the given numbers is 2 x 3 x 3 x 2 x 3 x 7 = 756

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/756

Therefore, the GCF of Fractions 105/36,150/54,210/126 is 15/756

Least Common Multiple of 36,54,126 with GCF Formula

Least Common Multiple of 36,54,126 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 36,54,126 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,54,126) = 18

common factors(in case of two or more numbers have common factors) = 18

GCF(36,54,126) x common factors =18 x 18 = 324

LCM(36,54,126) = ( 36 × 54 × 126 ) / 324

LCM(36,54,126) = 244944 / 324

LCM(36,54,126) = 756


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 105/36, 150/54, 210/126

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 105/36, 150/54, 210/126?

Answer: GCF of Numerators as per given numbers 105/36, 150/54, 210/126 is

GCF of Numerators i.e. for 105,150,210 is 15

LCM of denominators i.e. for 36,54,126 is 756.

Thus, GCF of Fractions is 15/756.Finally, GCF of Fractions for 105/36, 150/54, 210/126 is 15/756.