How to Find GCF of 69/238, 13/973, 408/493?

GCF of 69/238, 13/973, 408/493

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 69/238, 13/973, 408/493 i.e 1/959378 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/238, 13/973, 408/493.

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 69/238,13/973,408/493?

Given fractions are 69/238,13/973,408/493

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 69/238,13/973,408/493, numerators are 69,13,408

Denominators are 238,973,493

The GCF of 69,13,408 is 1 .

LCM of 238,973,493 is 959378.

The greatest common factor of 69/238,13/973,408/493 = [GCF of 69,13,408]/[LCM of 238,973,493]= 1/959378

Therefore, the GCF of 69/238,13/973,408/493 is 1/959378.

Greatest Common Factor of 69,13,408

To find the highest common factor of 69,13,408, we have to find the factors of both numbers and list the highest common factor.

The factors of 69 are 1, 3, 23, 69

The factors of 13 are 1, 13

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

The HCF of 69,13,408 is 1.

Lets's calculate GCF of 69,13,408

Greatest Common Factor (GCF) of 69,13,408 By Common Division

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

Greatest Common Factor of 69,13,408 By Matching Biggest Common Factor Method

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 13

1,13

Now, list down the factors of 408

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

Greatest Common Factor

We found the factors 69,13,408 . The biggest common factor number is the GCF number.
So the greatest common factor 69,13,408 is 1.

Lets's calculate LCM of 238,973,493

Lowest Common Multiple of 238,973,493 using Common Division

7	238, 973, 493
17	34, 139, 493
	2, 139, 29

∴ So the LCM of the given numbers is 7 x 17 x 2 x 139 x 29 = 959378

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/959378

Therefore, the GCF of Fractions 69/238,13/973,408/493 is 1/959378

Least Common Multiple of 238,973,493 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 238,973,493 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(238,973,493) = 1

common factors(in case of two or more numbers have common factors) = 119

GCF(238,973,493) x common factors =1 x 119 = 119

LCM(238,973,493) = ( 238 × 973 × 493 ) / 119

LCM(238,973,493) = 114165982 / 119

LCM(238,973,493) = 959378

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 69/238, 13/973, 408/493

1. What is the HCF of 69,13,408?

The HCF of 69,13,408 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 69/238, 13/973, 408/493?

Answer: GCF of Numerators as per given numbers 69/238, 13/973, 408/493 is

GCF of Numerators i.e. for 69,13,408 is 1

LCM of denominators i.e. for 238,973,493 is 959378.

Thus, GCF of Fractions is 1/959378.Finally, GCF of Fractions for 69/238, 13/973, 408/493 is 1/959378.