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GCF of 582/171, 512/788

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 582/171, 512/788 i.e 2/134748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 582/171, 512/788.

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 582/171,512/788?

Given fractions are 582/171,512/788

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 582/171,512/788, numerators are 582,512

Denominators are 171,788

The GCF of 582,512 is 2 .

LCM of 171,788 is 134748.

The greatest common factor of 582/171,512/788 = [GCF of 582,512]/[LCM of 171,788]= 2/134748

Therefore, the GCF of 582/171,512/788 is 2/134748.

Greatest Common Factor of 582,512

To find the highest common factor of 582,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 582,512 is 2.

Lets's calculate GCF of 582,512

Greatest Common Factor (GCF) of 582,512 By Common Division

2 582, 512
291, 256

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

Greatest Common Factor of 582,512 By Matching Biggest Common Factor Method

Greatest Common Factor of 582,512 By Matching Biggest Common Factor Method

Now, list down the factors of 582

:

1,2,3,6,97,194,291,582

Now, list down the factors of 512

:

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 582,512 . The biggest common factor number is the GCF number.
So the greatest common factor 582,512 is 2.

Lets's calculate LCM of 171,788

Lowest Common Multiple of 171,788 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 134748

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/134748

Therefore, the GCF of Fractions 582/171,512/788 is 2/134748

Least Common Multiple of 171,788 with GCF Formula

Least Common Multiple of 171,788 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 171,788 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(171,788) = 1

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

GCF(171,788) x common factors =1 x 1 = 1

LCM(171,788) = ( 171 × 788 ) / 1

LCM(171,788) = 134748 / 1

LCM(171,788) = 134748


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FAQs on GCF of Fractions of 582/171, 512/788

1. What is the HCF of 582,512?

The HCF of 582,512 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 582/171, 512/788?

Answer: GCF of Numerators as per given numbers 582/171, 512/788 is

GCF of Numerators i.e. for 582,512 is 2

LCM of denominators i.e. for 171,788 is 134748.

Thus, GCF of Fractions is 2/134748.Finally, GCF of Fractions for 582/171, 512/788 is 2/134748.