Greatest Common Factor of 58/342, 406/405

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 58/342, 406/405

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 58/342,406/405

Given fractions are 58/342,406/405

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 58,406

Greatest Common Factor of Numerators i.e. GCF of 58,406 is 58 .

LCM of Denominators means LCM of 342,405 as per the given fractions.

LCM of 342,405 is 15390 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 58,406

GCF of Fractions 58/342,406/405 is 58/15390

2 58, 406
29 29, 203
1, 7

∴ So the GCF of the given numbers is 2 x 29 = 58

Greatest Common Factor of 58,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 58,406 By Matching Biggest Common Factor Method

Factors of 58

List of positive integer factors of 58 that divides 58 without a remainder.

1,2,29,58

Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 58,406 . The biggest common factor number is the GCF number.
So the greatest common factor 58,406 is 58.

Lets's calculate LCM of 342,405

3 342, 405
3 114, 135
38, 45

∴ So the LCM of the given numbers is 3 x 3 x 38 x 45 = 15390

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/15390

Therefore, the GCF of Fractions 58/342,406/405 is 58/15390

Least Common Multiple of 342,405 with GCF Formula

Least Common Multiple of 342,405 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 342,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(342,405) = 9

common factors(in case of two or more numbers have common factors) = 1

GCF(342,405) x common factors =9 x 1 = 9

LCM(342,405) = ( 342 × 405 ) / 9

LCM(342,405) = 138510 / 9

LCM(342,405) = 15390


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 58/342, 406/405

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 58/342, 406/405?

Answer: GCF of Numerators as per given numbers 58/342, 406/405 is

GCF of Numerators i.e. for 58,406 is 58

LCM of denominators i.e. for 342,405 is 15390.

Thus, GCF of Fractions is 58/15390.Finally, GCF of Fractions for 58/342, 406/405 is 58/15390.