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GCF of 466/83, 578/7184

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 466/83, 578/7184 i.e 2/596272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 466/83, 578/7184.

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 466/83,578/7184?

Given fractions are 466/83,578/7184

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 466/83,578/7184, numerators are 466,578

Denominators are 83,7184

The GCF of 466,578 is 2 .

LCM of 83,7184 is 596272.

The greatest common factor of 466/83,578/7184 = [GCF of 466,578]/[LCM of 83,7184]= 2/596272

Therefore, the GCF of 466/83,578/7184 is 2/596272.

Greatest Common Factor of 466,578

To find the highest common factor of 466,578, we have to find the factors of both numbers and list the highest common factor.

The factors of 466 are 1, 2, 233, 466

The factors of 578 are 1, 2, 17, 34, 289, 578

The HCF of 466,578 is 2.

Lets's calculate GCF of 466,578

Greatest Common Factor (GCF) of 466,578 By Common Division

2 466, 578
233, 289

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

Greatest Common Factor of 466,578 By Matching Biggest Common Factor Method

Greatest Common Factor of 466,578 By Matching Biggest Common Factor Method

Now, list down the factors of 466

:

1,2,233,466

Now, list down the factors of 578

:

1,2,17,34,289,578

Greatest Common Factor

We found the factors 466,578 . The biggest common factor number is the GCF number.
So the greatest common factor 466,578 is 2.

Lets's calculate LCM of 83,7184

Lowest Common Multiple of 83,7184 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 596272

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/596272

Therefore, the GCF of Fractions 466/83,578/7184 is 2/596272

Least Common Multiple of 83,7184 with GCF Formula

Least Common Multiple of 83,7184 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 83,7184 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,7184) = 1

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

GCF(83,7184) x common factors =1 x 1 = 1

LCM(83,7184) = ( 83 × 7184 ) / 1

LCM(83,7184) = 596272 / 1

LCM(83,7184) = 596272


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FAQs on GCF of Fractions of 466/83, 578/7184

1. What is the HCF of 466,578?

The HCF of 466,578 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 466/83, 578/7184?

Answer: GCF of Numerators as per given numbers 466/83, 578/7184 is

GCF of Numerators i.e. for 466,578 is 2

LCM of denominators i.e. for 83,7184 is 596272.

Thus, GCF of Fractions is 2/596272.Finally, GCF of Fractions for 466/83, 578/7184 is 2/596272.