How to Find GCF of 868/506, 409/404?

GCF of 868/506, 409/404

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 868/506, 409/404 i.e 1/102212 easily. The following is the detailed procedure to determine the greatest common factor of fractions 868/506, 409/404.

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 868/506,409/404?

Given fractions are 868/506,409/404

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 868/506,409/404, numerators are 868,409

Denominators are 506,404

The GCF of 868,409 is 1 .

LCM of 506,404 is 102212.

The greatest common factor of 868/506,409/404 = [GCF of 868,409]/[LCM of 506,404]= 1/102212

Therefore, the GCF of 868/506,409/404 is 1/102212.

Greatest Common Factor of 868,409

To find the highest common factor of 868,409, we have to find the factors of both numbers and list the highest common factor.

The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868

The factors of 409 are 1, 409

The HCF of 868,409 is 1.

Lets's calculate GCF of 868,409

Greatest Common Factor (GCF) of 868,409 By Common Division

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

Greatest Common Factor of 868,409 By Matching Biggest Common Factor Method

Now, list down the factors of 868

1,2,4,7,14,28,31,62,124,217,434,868

Now, list down the factors of 409

1,409

Greatest Common Factor

We found the factors 868,409 . The biggest common factor number is the GCF number.
So the greatest common factor 868,409 is 1.

Lets's calculate LCM of 506,404

Lowest Common Multiple of 506,404 using Common Division

2	506, 404
	253, 202

∴ So the LCM of the given numbers is 2 x 253 x 202 = 102212

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/102212

Therefore, the GCF of Fractions 868/506,409/404 is 1/102212

Least Common Multiple of 506,404 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 506,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(506,404) = 2

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

GCF(506,404) x common factors =2 x 1 = 2

LCM(506,404) = ( 506 × 404 ) / 2

LCM(506,404) = 204424 / 2

LCM(506,404) = 102212

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FAQs on GCF of Fractions of 868/506, 409/404

1. What is the HCF of 868,409?

The HCF of 868,409 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 868/506, 409/404?

Answer: GCF of Numerators as per given numbers 868/506, 409/404 is

GCF of Numerators i.e. for 868,409 is 1

LCM of denominators i.e. for 506,404 is 102212.

Thus, GCF of Fractions is 1/102212.Finally, GCF of Fractions for 868/506, 409/404 is 1/102212.