Greatest Common Factor of 38/42, 40/25, 42/70, 82/19

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 38/42, 40/25, 42/70, 82/19

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 38/42,40/25,42/70,82/19

Given fractions are 38/42,40/25,42/70,82/19

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 38,40,42,82

Greatest Common Factor of Numerators i.e. GCF of 38,40,42,82 is 2 .

LCM of Denominators means LCM of 42,25,70,19 as per the given fractions.

LCM of 42,25,70,19 is 19950 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 38,40,42,82

GCF of Fractions 38/42,40/25,42/70,82/19 is 2/19950

2 38, 40, 42, 82
19, 20, 21, 41

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

Greatest Common Factor of 38,40,42,82 By Matching Biggest Common Factor Method

Greatest Common Factor of 38,40,42,82 By Matching Biggest Common Factor Method

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

Greatest Common Factor

We found the factors 38,40,42,82 . The biggest common factor number is the GCF number.
So the greatest common factor 38,40,42,82 is 2.

Lets's calculate LCM of 42,25,70,19

2 42, 25, 70, 19
5 21, 25, 35, 19
7 21, 5, 7, 19
3, 5, 1, 19

∴ So the LCM of the given numbers is 2 x 5 x 7 x 3 x 5 x 1 x 19 = 19950

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/19950

Therefore, the GCF of Fractions 38/42,40/25,42/70,82/19 is 2/19950

Least Common Multiple of 42,25,70,19 with GCF Formula

Least Common Multiple of 42,25,70,19 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 42,25,70,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,25,70,19) = 1

common factors(in case of two or more numbers have common factors) = 70

GCF(42,25,70,19) x common factors =1 x 70 = 70

LCM(42,25,70,19) = ( 42 × 25 × 70 × 19 ) / 70

LCM(42,25,70,19) = 1396500 / 70

LCM(42,25,70,19) = 19950


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 38/42, 40/25, 42/70, 82/19

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 38/42, 40/25, 42/70, 82/19?

Answer: GCF of Numerators as per given numbers 38/42, 40/25, 42/70, 82/19 is

GCF of Numerators i.e. for 38,40,42,82 is 2

LCM of denominators i.e. for 42,25,70,19 is 19950.

Thus, GCF of Fractions is 2/19950.Finally, GCF of Fractions for 38/42, 40/25, 42/70, 82/19 is 2/19950.