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GCF of 209/237, 1949/9738

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 209/237, 1949/9738 i.e 1/769302 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/237, 1949/9738.

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 209/237,1949/9738?

Given fractions are 209/237,1949/9738

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 209/237,1949/9738, numerators are 209,1949

Denominators are 237,9738

The GCF of 209,1949 is 1 .

LCM of 237,9738 is 769302.

The greatest common factor of 209/237,1949/9738 = [GCF of 209,1949]/[LCM of 237,9738]= 1/769302

Therefore, the GCF of 209/237,1949/9738 is 1/769302.

Greatest Common Factor of 209,1949

To find the highest common factor of 209,1949, we have to find the factors of both numbers and list the highest common factor.

The factors of 209 are 1, 11, 19, 209

The factors of 1949 are 1, 1949

The HCF of 209,1949 is 1.

Lets's calculate GCF of 209,1949

Greatest Common Factor (GCF) of 209,1949 By Common Division

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

Greatest Common Factor of 209,1949 By Matching Biggest Common Factor Method

Greatest Common Factor of 209,1949 By Matching Biggest Common Factor Method

Now, list down the factors of 209

:

1,11,19,209

Now, list down the factors of 1949

:

1,1949

Greatest Common Factor

We found the factors 209,1949 . The biggest common factor number is the GCF number.
So the greatest common factor 209,1949 is 1.

Lets's calculate LCM of 237,9738

Lowest Common Multiple of 237,9738 using Common Division

3 237, 9738
79, 3246

∴ So the LCM of the given numbers is 3 x 79 x 3246 = 769302

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/769302

Therefore, the GCF of Fractions 209/237,1949/9738 is 1/769302

Least Common Multiple of 237,9738 with GCF Formula

Least Common Multiple of 237,9738 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 237,9738 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(237,9738) = 3

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

GCF(237,9738) x common factors =3 x 1 = 3

LCM(237,9738) = ( 237 × 9738 ) / 3

LCM(237,9738) = 2307906 / 3

LCM(237,9738) = 769302


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FAQs on GCF of Fractions of 209/237, 1949/9738

1. What is the HCF of 209,1949?

The HCF of 209,1949 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 209/237, 1949/9738?

Answer: GCF of Numerators as per given numbers 209/237, 1949/9738 is

GCF of Numerators i.e. for 209,1949 is 1

LCM of denominators i.e. for 237,9738 is 769302.

Thus, GCF of Fractions is 1/769302.Finally, GCF of Fractions for 209/237, 1949/9738 is 1/769302.