How to Find GCF of 1831/648, 1961/116?

GCF of 1831/648, 1961/116

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 1831/648, 1961/116 i.e 1/18792 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1831/648, 1961/116.

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 1831/648,1961/116?

Given fractions are 1831/648,1961/116

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 1831/648,1961/116, numerators are 1831,1961

Denominators are 648,116

The GCF of 1831,1961 is 1 .

LCM of 648,116 is 18792.

The greatest common factor of 1831/648,1961/116 = [GCF of 1831,1961]/[LCM of 648,116]= 1/18792

Therefore, the GCF of 1831/648,1961/116 is 1/18792.

Greatest Common Factor of 1831,1961

To find the highest common factor of 1831,1961, we have to find the factors of both numbers and list the highest common factor.

The factors of 1831 are 1, 1831

The factors of 1961 are 1, 37, 53, 1961

The HCF of 1831,1961 is 1.

Lets's calculate GCF of 1831,1961

Greatest Common Factor (GCF) of 1831,1961 By Common Division

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

Greatest Common Factor of 1831,1961 By Matching Biggest Common Factor Method

Now, list down the factors of 1831

1,1831

Now, list down the factors of 1961

1,37,53,1961

Greatest Common Factor

We found the factors 1831,1961 . The biggest common factor number is the GCF number.
So the greatest common factor 1831,1961 is 1.

Lets's calculate LCM of 648,116

Lowest Common Multiple of 648,116 using Common Division

2	648, 116
2	324, 58
	162, 29

∴ So the LCM of the given numbers is 2 x 2 x 162 x 29 = 18792

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18792

Therefore, the GCF of Fractions 1831/648,1961/116 is 1/18792

Least Common Multiple of 648,116 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 648,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(648,116) = 4

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

GCF(648,116) x common factors =4 x 1 = 4

LCM(648,116) = ( 648 × 116 ) / 4

LCM(648,116) = 75168 / 4

LCM(648,116) = 18792

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 1831/648, 1961/116

1. What is the HCF of 1831,1961?

The HCF of 1831,1961 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 1831/648, 1961/116?

Answer: GCF of Numerators as per given numbers 1831/648, 1961/116 is

GCF of Numerators i.e. for 1831,1961 is 1

LCM of denominators i.e. for 648,116 is 18792.

Thus, GCF of Fractions is 1/18792.Finally, GCF of Fractions for 1831/648, 1961/116 is 1/18792.