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GCF of 557/470, 550/678

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 557/470, 550/678 i.e 1/159330 easily. The following is the detailed procedure to determine the greatest common factor of fractions 557/470, 550/678.

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 557/470,550/678?

Given fractions are 557/470,550/678

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 557/470,550/678, numerators are 557,550

Denominators are 470,678

The GCF of 557,550 is 1 .

LCM of 470,678 is 159330.

The greatest common factor of 557/470,550/678 = [GCF of 557,550]/[LCM of 470,678]= 1/159330

Therefore, the GCF of 557/470,550/678 is 1/159330.

Greatest Common Factor of 557,550

To find the highest common factor of 557,550, we have to find the factors of both numbers and list the highest common factor.

The factors of 557 are 1, 557

The factors of 550 are 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550

The HCF of 557,550 is 1.

Lets's calculate GCF of 557,550

Greatest Common Factor (GCF) of 557,550 By Common Division

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

Greatest Common Factor of 557,550 By Matching Biggest Common Factor Method

Greatest Common Factor of 557,550 By Matching Biggest Common Factor Method

Now, list down the factors of 557

:

1,557

Now, list down the factors of 550

:

1,2,5,10,11,22,25,50,55,110,275,550

Greatest Common Factor

We found the factors 557,550 . The biggest common factor number is the GCF number.
So the greatest common factor 557,550 is 1.

Lets's calculate LCM of 470,678

Lowest Common Multiple of 470,678 using Common Division

2 470, 678
235, 339

∴ So the LCM of the given numbers is 2 x 235 x 339 = 159330

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/159330

Therefore, the GCF of Fractions 557/470,550/678 is 1/159330

Least Common Multiple of 470,678 with GCF Formula

Least Common Multiple of 470,678 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 470,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,678) = 2

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

GCF(470,678) x common factors =2 x 1 = 2

LCM(470,678) = ( 470 × 678 ) / 2

LCM(470,678) = 318660 / 2

LCM(470,678) = 159330


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FAQs on GCF of Fractions of 557/470, 550/678

1. What is the HCF of 557,550?

The HCF of 557,550 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 557/470, 550/678?

Answer: GCF of Numerators as per given numbers 557/470, 550/678 is

GCF of Numerators i.e. for 557,550 is 1

LCM of denominators i.e. for 470,678 is 159330.

Thus, GCF of Fractions is 1/159330.Finally, GCF of Fractions for 557/470, 550/678 is 1/159330.