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GCF of 506/26, 308/404

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 506/26, 308/404 i.e 22/5252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/26, 308/404.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 506/26,308/404?

Given fractions are 506/26,308/404

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 506/26,308/404, numerators are 506,308

Denominators are 26,404

The GCF of 506,308 is 22 .

LCM of 26,404 is 5252.

The greatest common factor of 506/26,308/404 = [GCF of 506,308]/[LCM of 26,404]= 22/5252

Therefore, the GCF of 506/26,308/404 is 22/5252.

Greatest Common Factor of 506,308

To find the highest common factor of 506,308, we have to find the factors of both numbers and list the highest common factor.

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The HCF of 506,308 is 22.

Lets's calculate GCF of 506,308

Greatest Common Factor (GCF) of 506,308 By Common Division

2 506, 308
11 253, 154
23, 14

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 506,308 By Matching Biggest Common Factor Method

Greatest Common Factor of 506,308 By Matching Biggest Common Factor Method

Now, list down the factors of 506

:

1,2,11,22,23,46,253,506

Now, list down the factors of 308

:

1,2,4,7,11,14,22,28,44,77,154,308

Greatest Common Factor

We found the factors 506,308 . The biggest common factor number is the GCF number.
So the greatest common factor 506,308 is 22.

Lets's calculate LCM of 26,404

Lowest Common Multiple of 26,404 using Common Division

2 26, 404
13, 202

∴ So the LCM of the given numbers is 2 x 13 x 202 = 5252

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/5252

Therefore, the GCF of Fractions 506/26,308/404 is 22/5252

Least Common Multiple of 26,404 with GCF Formula

Least Common Multiple of 26,404 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 26,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(26,404) = 2

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

GCF(26,404) x common factors =2 x 1 = 2

LCM(26,404) = ( 26 × 404 ) / 2

LCM(26,404) = 10504 / 2

LCM(26,404) = 5252


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FAQs on GCF of Fractions of 506/26, 308/404

1. What is the HCF of 506,308?

The HCF of 506,308 is 22

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 506/26, 308/404?

Answer: GCF of Numerators as per given numbers 506/26, 308/404 is

GCF of Numerators i.e. for 506,308 is 22

LCM of denominators i.e. for 26,404 is 5252.

Thus, GCF of Fractions is 22/5252.Finally, GCF of Fractions for 506/26, 308/404 is 22/5252.