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GCF of 523/142, 102/208

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 523/142, 102/208 i.e 1/14768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 523/142, 102/208.

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 523/142,102/208?

Given fractions are 523/142,102/208

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 523/142,102/208, numerators are 523,102

Denominators are 142,208

The GCF of 523,102 is 1 .

LCM of 142,208 is 14768.

The greatest common factor of 523/142,102/208 = [GCF of 523,102]/[LCM of 142,208]= 1/14768

Therefore, the GCF of 523/142,102/208 is 1/14768.

Greatest Common Factor of 523,102

To find the highest common factor of 523,102, we have to find the factors of both numbers and list the highest common factor.

The factors of 523 are 1, 523

The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102

The HCF of 523,102 is 1.

Lets's calculate GCF of 523,102

Greatest Common Factor (GCF) of 523,102 By Common Division

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

Greatest Common Factor of 523,102 By Matching Biggest Common Factor Method

Greatest Common Factor of 523,102 By Matching Biggest Common Factor Method

Now, list down the factors of 523

:

1,523

Now, list down the factors of 102

:

1,2,3,6,17,34,51,102

Greatest Common Factor

We found the factors 523,102 . The biggest common factor number is the GCF number.
So the greatest common factor 523,102 is 1.

Lets's calculate LCM of 142,208

Lowest Common Multiple of 142,208 using Common Division

2 142, 208
71, 104

∴ So the LCM of the given numbers is 2 x 71 x 104 = 14768

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14768

Therefore, the GCF of Fractions 523/142,102/208 is 1/14768

Least Common Multiple of 142,208 with GCF Formula

Least Common Multiple of 142,208 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 142,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(142,208) = 2

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

GCF(142,208) x common factors =2 x 1 = 2

LCM(142,208) = ( 142 × 208 ) / 2

LCM(142,208) = 29536 / 2

LCM(142,208) = 14768


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FAQs on GCF of Fractions of 523/142, 102/208

1. What is the HCF of 523,102?

The HCF of 523,102 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 523/142, 102/208?

Answer: GCF of Numerators as per given numbers 523/142, 102/208 is

GCF of Numerators i.e. for 523,102 is 1

LCM of denominators i.e. for 142,208 is 14768.

Thus, GCF of Fractions is 1/14768.Finally, GCF of Fractions for 523/142, 102/208 is 1/14768.