How to Find GCF of 2138/108, 1927/7148?

GCF of 2138/108, 1927/7148

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 2138/108, 1927/7148 i.e 1/192996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2138/108, 1927/7148.

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 2138/108,1927/7148?

Given fractions are 2138/108,1927/7148

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 2138/108,1927/7148, numerators are 2138,1927

Denominators are 108,7148

The GCF of 2138,1927 is 1 .

LCM of 108,7148 is 192996.

The greatest common factor of 2138/108,1927/7148 = [GCF of 2138,1927]/[LCM of 108,7148]= 1/192996

Therefore, the GCF of 2138/108,1927/7148 is 1/192996.

Greatest Common Factor of 2138,1927

To find the highest common factor of 2138,1927, we have to find the factors of both numbers and list the highest common factor.

The factors of 2138 are 1, 2, 1069, 2138

The factors of 1927 are 1, 41, 47, 1927

The HCF of 2138,1927 is 1.

Lets's calculate GCF of 2138,1927

Greatest Common Factor (GCF) of 2138,1927 By Common Division

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

Greatest Common Factor of 2138,1927 By Matching Biggest Common Factor Method

Now, list down the factors of 2138

1,2,1069,2138

Now, list down the factors of 1927

1,41,47,1927

Greatest Common Factor

We found the factors 2138,1927 . The biggest common factor number is the GCF number.
So the greatest common factor 2138,1927 is 1.

Lets's calculate LCM of 108,7148

Lowest Common Multiple of 108,7148 using Common Division

2	108, 7148
2	54, 3574
	27, 1787

∴ So the LCM of the given numbers is 2 x 2 x 27 x 1787 = 192996

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/192996

Therefore, the GCF of Fractions 2138/108,1927/7148 is 1/192996

Least Common Multiple of 108,7148 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 108,7148 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(108,7148) = 4

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

GCF(108,7148) x common factors =4 x 1 = 4

LCM(108,7148) = ( 108 × 7148 ) / 4

LCM(108,7148) = 771984 / 4

LCM(108,7148) = 192996

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FAQs on GCF of Fractions of 2138/108, 1927/7148

1. What is the HCF of 2138,1927?

The HCF of 2138,1927 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 2138/108, 1927/7148?

Answer: GCF of Numerators as per given numbers 2138/108, 1927/7148 is

GCF of Numerators i.e. for 2138,1927 is 1

LCM of denominators i.e. for 108,7148 is 192996.

Thus, GCF of Fractions is 1/192996.Finally, GCF of Fractions for 2138/108, 1927/7148 is 1/192996.