How to Find GCF of 2113/164, 1938/9810?

GCF of 2113/164, 1938/9810

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 2113/164, 1938/9810 i.e 1/804420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2113/164, 1938/9810.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 2113/164,1938/9810?

Given fractions are 2113/164,1938/9810

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 2113/164,1938/9810, numerators are 2113,1938

Denominators are 164,9810

The GCF of 2113,1938 is 1 .

LCM of 164,9810 is 804420.

The greatest common factor of 2113/164,1938/9810 = [GCF of 2113,1938]/[LCM of 164,9810]= 1/804420

Therefore, the GCF of 2113/164,1938/9810 is 1/804420.

Greatest Common Factor of 2113,1938

To find the highest common factor of 2113,1938, we have to find the factors of both numbers and list the highest common factor.

The factors of 2113 are 1, 2113

The factors of 1938 are 1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 646, 969, 1938

The HCF of 2113,1938 is 1.

Lets's calculate GCF of 2113,1938

Greatest Common Factor (GCF) of 2113,1938 By Common Division

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

Greatest Common Factor of 2113,1938 By Matching Biggest Common Factor Method

Now, list down the factors of 2113

1,2113

Now, list down the factors of 1938

1,2,3,6,17,19,34,38,51,57,102,114,323,646,969,1938

Greatest Common Factor

We found the factors 2113,1938 . The biggest common factor number is the GCF number.
So the greatest common factor 2113,1938 is 1.

Lets's calculate LCM of 164,9810

Lowest Common Multiple of 164,9810 using Common Division

2	164, 9810
	82, 4905

∴ So the LCM of the given numbers is 2 x 82 x 4905 = 804420

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/804420

Therefore, the GCF of Fractions 2113/164,1938/9810 is 1/804420

Least Common Multiple of 164,9810 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 164,9810 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(164,9810) = 2

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

GCF(164,9810) x common factors =2 x 1 = 2

LCM(164,9810) = ( 164 × 9810 ) / 2

LCM(164,9810) = 1608840 / 2

LCM(164,9810) = 804420

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FAQs on GCF of Fractions of 2113/164, 1938/9810

1. What is the HCF of 2113,1938?

The HCF of 2113,1938 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 2113/164, 1938/9810?

Answer: GCF of Numerators as per given numbers 2113/164, 1938/9810 is

GCF of Numerators i.e. for 2113,1938 is 1

LCM of denominators i.e. for 164,9810 is 804420.

Thus, GCF of Fractions is 1/804420.Finally, GCF of Fractions for 2113/164, 1938/9810 is 1/804420.