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GCF of 658/784, 563/226

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 658/784, 563/226 i.e 1/88592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 658/784, 563/226.

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 658/784,563/226?

Given fractions are 658/784,563/226

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 658/784,563/226, numerators are 658,563

Denominators are 784,226

The GCF of 658,563 is 1 .

LCM of 784,226 is 88592.

The greatest common factor of 658/784,563/226 = [GCF of 658,563]/[LCM of 784,226]= 1/88592

Therefore, the GCF of 658/784,563/226 is 1/88592.

Greatest Common Factor of 658,563

To find the highest common factor of 658,563, we have to find the factors of both numbers and list the highest common factor.

The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658

The factors of 563 are 1, 563

The HCF of 658,563 is 1.

Lets's calculate GCF of 658,563

Greatest Common Factor (GCF) of 658,563 By Common Division

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

Greatest Common Factor of 658,563 By Matching Biggest Common Factor Method

Greatest Common Factor of 658,563 By Matching Biggest Common Factor Method

Now, list down the factors of 658

:

1,2,7,14,47,94,329,658

Now, list down the factors of 563

:

1,563

Greatest Common Factor

We found the factors 658,563 . The biggest common factor number is the GCF number.
So the greatest common factor 658,563 is 1.

Lets's calculate LCM of 784,226

Lowest Common Multiple of 784,226 using Common Division

2 784, 226
392, 113

∴ So the LCM of the given numbers is 2 x 392 x 113 = 88592

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/88592

Therefore, the GCF of Fractions 658/784,563/226 is 1/88592

Least Common Multiple of 784,226 with GCF Formula

Least Common Multiple of 784,226 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 784,226 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(784,226) = 2

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

GCF(784,226) x common factors =2 x 1 = 2

LCM(784,226) = ( 784 × 226 ) / 2

LCM(784,226) = 177184 / 2

LCM(784,226) = 88592


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FAQs on GCF of Fractions of 658/784, 563/226

1. What is the HCF of 658,563?

The HCF of 658,563 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 658/784, 563/226?

Answer: GCF of Numerators as per given numbers 658/784, 563/226 is

GCF of Numerators i.e. for 658,563 is 1

LCM of denominators i.e. for 784,226 is 88592.

Thus, GCF of Fractions is 1/88592.Finally, GCF of Fractions for 658/784, 563/226 is 1/88592.