Greatest Common Factor of 84/29, 45/52, 75/19, 15/78

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 84/29, 45/52, 75/19, 15/78

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 84/29,45/52,75/19,15/78

Given fractions are 84/29,45/52,75/19,15/78

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 84,45,75,15

Greatest Common Factor of Numerators i.e. GCF of 84,45,75,15 is 3 .

LCM of Denominators means LCM of 29,52,19,78 as per the given fractions.

LCM of 29,52,19,78 is 85956 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 84,45,75,15

GCF of Fractions 84/29,45/52,75/19,15/78 is 3/85956

3 84, 45, 75, 15
28, 15, 25, 5

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 84,45,75,15 By Matching Biggest Common Factor Method

Greatest Common Factor of 84,45,75,15 By Matching Biggest Common Factor Method

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 75

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

1,3,5,15,25,75

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1,3,5,15

Greatest Common Factor

We found the factors 84,45,75,15 . The biggest common factor number is the GCF number.
So the greatest common factor 84,45,75,15 is 3.

Lets's calculate LCM of 29,52,19,78

2 29, 52, 19, 78
13 29, 26, 19, 39
29, 2, 19, 3

∴ So the LCM of the given numbers is 2 x 13 x 29 x 2 x 19 x 3 = 85956

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/85956

Therefore, the GCF of Fractions 84/29,45/52,75/19,15/78 is 3/85956

Least Common Multiple of 29,52,19,78 with GCF Formula

Least Common Multiple of 29,52,19,78 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 29,52,19,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(29,52,19,78) = 1

common factors(in case of two or more numbers have common factors) = 26

GCF(29,52,19,78) x common factors =1 x 26 = 26

LCM(29,52,19,78) = ( 29 × 52 × 19 × 78 ) / 26

LCM(29,52,19,78) = 2234856 / 26

LCM(29,52,19,78) = 85956


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 84/29, 45/52, 75/19, 15/78

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 84/29, 45/52, 75/19, 15/78?

Answer: GCF of Numerators as per given numbers 84/29, 45/52, 75/19, 15/78 is

GCF of Numerators i.e. for 84,45,75,15 is 3

LCM of denominators i.e. for 29,52,19,78 is 85956.

Thus, GCF of Fractions is 3/85956.Finally, GCF of Fractions for 84/29, 45/52, 75/19, 15/78 is 3/85956.