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GCF of 514/74, 592/404

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 514/74, 592/404 i.e 2/14948 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/74, 592/404.

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 514/74,592/404?

Given fractions are 514/74,592/404

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 514/74,592/404, numerators are 514,592

Denominators are 74,404

The GCF of 514,592 is 2 .

LCM of 74,404 is 14948.

The greatest common factor of 514/74,592/404 = [GCF of 514,592]/[LCM of 74,404]= 2/14948

Therefore, the GCF of 514/74,592/404 is 2/14948.

Greatest Common Factor of 514,592

To find the highest common factor of 514,592, we have to find the factors of both numbers and list the highest common factor.

The factors of 514 are 1, 2, 257, 514

The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592

The HCF of 514,592 is 2.

Lets's calculate GCF of 514,592

Greatest Common Factor (GCF) of 514,592 By Common Division

2 514, 592
257, 296

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 514,592 By Matching Biggest Common Factor Method

Greatest Common Factor of 514,592 By Matching Biggest Common Factor Method

Now, list down the factors of 514

:

1,2,257,514

Now, list down the factors of 592

:

1,2,4,8,16,37,74,148,296,592

Greatest Common Factor

We found the factors 514,592 . The biggest common factor number is the GCF number.
So the greatest common factor 514,592 is 2.

Lets's calculate LCM of 74,404

Lowest Common Multiple of 74,404 using Common Division

2 74, 404
37, 202

∴ So the LCM of the given numbers is 2 x 37 x 202 = 14948

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14948

Therefore, the GCF of Fractions 514/74,592/404 is 2/14948

Least Common Multiple of 74,404 with GCF Formula

Least Common Multiple of 74,404 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 74,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,404) = 2

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

GCF(74,404) x common factors =2 x 1 = 2

LCM(74,404) = ( 74 × 404 ) / 2

LCM(74,404) = 29896 / 2

LCM(74,404) = 14948


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FAQs on GCF of Fractions of 514/74, 592/404

1. What is the HCF of 514,592?

The HCF of 514,592 is 2

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 514/74, 592/404?

Answer: GCF of Numerators as per given numbers 514/74, 592/404 is

GCF of Numerators i.e. for 514,592 is 2

LCM of denominators i.e. for 74,404 is 14948.

Thus, GCF of Fractions is 2/14948.Finally, GCF of Fractions for 514/74, 592/404 is 2/14948.