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GCF of 646/674, 578/932

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 646/674, 578/932 i.e 34/314084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 646/674, 578/932.

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 646/674,578/932?

Given fractions are 646/674,578/932

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 646/674,578/932, numerators are 646,578

Denominators are 674,932

The GCF of 646,578 is 34 .

LCM of 674,932 is 314084.

The greatest common factor of 646/674,578/932 = [GCF of 646,578]/[LCM of 674,932]= 34/314084

Therefore, the GCF of 646/674,578/932 is 34/314084.

Greatest Common Factor of 646,578

To find the highest common factor of 646,578, we have to find the factors of both numbers and list the highest common factor.

The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646

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

The HCF of 646,578 is 34.

Lets's calculate GCF of 646,578

Greatest Common Factor (GCF) of 646,578 By Common Division

2 646, 578
17 323, 289
19, 17

∴ So the GCF of the given numbers is 2 x 17 = 34

Greatest Common Factor of 646,578 By Matching Biggest Common Factor Method

Greatest Common Factor of 646,578 By Matching Biggest Common Factor Method

Now, list down the factors of 646

:

1,2,17,19,34,38,323,646

Now, list down the factors of 578

:

1,2,17,34,289,578

Greatest Common Factor

We found the factors 646,578 . The biggest common factor number is the GCF number.
So the greatest common factor 646,578 is 34.

Lets's calculate LCM of 674,932

Lowest Common Multiple of 674,932 using Common Division

2 674, 932
337, 466

∴ So the LCM of the given numbers is 2 x 337 x 466 = 314084

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/314084

Therefore, the GCF of Fractions 646/674,578/932 is 34/314084

Least Common Multiple of 674,932 with GCF Formula

Least Common Multiple of 674,932 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 674,932 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(674,932) = 2

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

GCF(674,932) x common factors =2 x 1 = 2

LCM(674,932) = ( 674 × 932 ) / 2

LCM(674,932) = 628168 / 2

LCM(674,932) = 314084


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FAQs on GCF of Fractions of 646/674, 578/932

1. What is the HCF of 646,578?

The HCF of 646,578 is 34

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 646/674, 578/932?

Answer: GCF of Numerators as per given numbers 646/674, 578/932 is

GCF of Numerators i.e. for 646,578 is 34

LCM of denominators i.e. for 674,932 is 314084.

Thus, GCF of Fractions is 34/314084.Finally, GCF of Fractions for 646/674, 578/932 is 34/314084.