How to Find GCF of 58/378, 401/308, 215/422?

GCF of 58/378, 401/308, 215/422

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 58/378, 401/308, 215/422 i.e 1/1754676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 58/378, 401/308, 215/422.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 58/378,401/308,215/422?

Given fractions are 58/378,401/308,215/422

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 58/378,401/308,215/422, numerators are 58,401,215

Denominators are 378,308,422

The GCF of 58,401,215 is 1 .

LCM of 378,308,422 is 1754676.

The greatest common factor of 58/378,401/308,215/422 = [GCF of 58,401,215]/[LCM of 378,308,422]= 1/1754676

Therefore, the GCF of 58/378,401/308,215/422 is 1/1754676.

Greatest Common Factor of 58,401,215

To find the highest common factor of 58,401,215, we have to find the factors of both numbers and list the highest common factor.

The factors of 58 are 1, 2, 29, 58

The factors of 401 are 1, 401

The factors of 215 are 1, 5, 43, 215

The HCF of 58,401,215 is 1.

Lets's calculate GCF of 58,401,215

Greatest Common Factor (GCF) of 58,401,215 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 58,401,215 By Matching Biggest Common Factor Method

Now, list down the factors of 58

1,2,29,58

Now, list down the factors of 401

1,401

Now, list down the factors of 215

1,5,43,215

Greatest Common Factor

We found the factors 58,401,215 . The biggest common factor number is the GCF number.
So the greatest common factor 58,401,215 is 1.

Lets's calculate LCM of 378,308,422

Lowest Common Multiple of 378,308,422 using Common Division

2	378, 308, 422
7	189, 154, 211
	27, 22, 211

∴ So the LCM of the given numbers is 2 x 7 x 27 x 22 x 211 = 1754676

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1754676

Therefore, the GCF of Fractions 58/378,401/308,215/422 is 1/1754676

Least Common Multiple of 378,308,422 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 378,308,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(378,308,422) = 2

common factors(in case of two or more numbers have common factors) = 14

GCF(378,308,422) x common factors =2 x 14 = 28

LCM(378,308,422) = ( 378 × 308 × 422 ) / 28

LCM(378,308,422) = 49130928 / 28

LCM(378,308,422) = 1754676

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 58/378, 401/308, 215/422

1. What is the HCF of 58,401,215?

The HCF of 58,401,215 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 58/378, 401/308, 215/422?

Answer: GCF of Numerators as per given numbers 58/378, 401/308, 215/422 is

GCF of Numerators i.e. for 58,401,215 is 1

LCM of denominators i.e. for 378,308,422 is 1754676.

Thus, GCF of Fractions is 1/1754676.Finally, GCF of Fractions for 58/378, 401/308, 215/422 is 1/1754676.