Greatest Common Factor of 144/36, 510/14, 334/75

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 144/36, 510/14, 334/75

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 144/36,510/14,334/75

Given fractions are 144/36,510/14,334/75

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 144,510,334

Greatest Common Factor of Numerators i.e. GCF of 144,510,334 is 2 .

LCM of Denominators means LCM of 36,14,75 as per the given fractions.

LCM of 36,14,75 is 6300 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 144,510,334

GCF of Fractions 144/36,510/14,334/75 is 2/6300

2 144, 510, 334
72, 255, 167

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 144,510,334 By Matching Biggest Common Factor Method

Greatest Common Factor of 144,510,334 By Matching Biggest Common Factor Method

Factors of 144

List of positive integer factors of 144 that divides 144 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Factors of 510

List of positive integer factors of 510 that divides 510 without a remainder.

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Factors of 334

List of positive integer factors of 334 that divides 334 without a remainder.

1,2,167,334

Greatest Common Factor

We found the factors 144,510,334 . The biggest common factor number is the GCF number.
So the greatest common factor 144,510,334 is 2.

Lets's calculate LCM of 36,14,75

2 36, 14, 75
3 18, 7, 75
6, 7, 25

∴ So the LCM of the given numbers is 2 x 3 x 6 x 7 x 25 = 6300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6300

Therefore, the GCF of Fractions 144/36,510/14,334/75 is 2/6300

Least Common Multiple of 36,14,75 with GCF Formula

Least Common Multiple of 36,14,75 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 36,14,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,14,75) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(36,14,75) x common factors =1 x 6 = 6

LCM(36,14,75) = ( 36 × 14 × 75 ) / 6

LCM(36,14,75) = 37800 / 6

LCM(36,14,75) = 6300


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 144/36, 510/14, 334/75

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 144/36, 510/14, 334/75?

Answer: GCF of Numerators as per given numbers 144/36, 510/14, 334/75 is

GCF of Numerators i.e. for 144,510,334 is 2

LCM of denominators i.e. for 36,14,75 is 6300.

Thus, GCF of Fractions is 2/6300.Finally, GCF of Fractions for 144/36, 510/14, 334/75 is 2/6300.