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GCF of 646/52, 209/789

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 646/52, 209/789 i.e 19/41028 easily. The following is the detailed procedure to determine the greatest common factor of fractions 646/52, 209/789.

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 646/52,209/789?

Given fractions are 646/52,209/789

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 646/52,209/789, numerators are 646,209

Denominators are 52,789

The GCF of 646,209 is 19 .

LCM of 52,789 is 41028.

The greatest common factor of 646/52,209/789 = [GCF of 646,209]/[LCM of 52,789]= 19/41028

Therefore, the GCF of 646/52,209/789 is 19/41028.

Greatest Common Factor of 646,209

To find the highest common factor of 646,209, 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 209 are 1, 11, 19, 209

The HCF of 646,209 is 19.

Lets's calculate GCF of 646,209

Greatest Common Factor (GCF) of 646,209 By Common Division

19 646, 209
34, 11

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 646,209 By Matching Biggest Common Factor Method

Greatest Common Factor of 646,209 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 209

:

1,11,19,209

Greatest Common Factor

We found the factors 646,209 . The biggest common factor number is the GCF number.
So the greatest common factor 646,209 is 19.

Lets's calculate LCM of 52,789

Lowest Common Multiple of 52,789 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 41028

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/41028

Therefore, the GCF of Fractions 646/52,209/789 is 19/41028

Least Common Multiple of 52,789 with GCF Formula

Least Common Multiple of 52,789 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 52,789 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,789) = 1

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

GCF(52,789) x common factors =1 x 1 = 1

LCM(52,789) = ( 52 × 789 ) / 1

LCM(52,789) = 41028 / 1

LCM(52,789) = 41028


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FAQs on GCF of Fractions of 646/52, 209/789

1. What is the HCF of 646,209?

The HCF of 646,209 is 19

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 646/52, 209/789?

Answer: GCF of Numerators as per given numbers 646/52, 209/789 is

GCF of Numerators i.e. for 646,209 is 19

LCM of denominators i.e. for 52,789 is 41028.

Thus, GCF of Fractions is 19/41028.Finally, GCF of Fractions for 646/52, 209/789 is 19/41028.