How to Find GCF of 1966/106, 6131/7802?

GCF of 1966/106, 6131/7802

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 1966/106, 6131/7802 i.e 1/413506 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1966/106, 6131/7802.

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 1966/106,6131/7802?

Given fractions are 1966/106,6131/7802

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 1966/106,6131/7802, numerators are 1966,6131

Denominators are 106,7802

The GCF of 1966,6131 is 1 .

LCM of 106,7802 is 413506.

The greatest common factor of 1966/106,6131/7802 = [GCF of 1966,6131]/[LCM of 106,7802]= 1/413506

Therefore, the GCF of 1966/106,6131/7802 is 1/413506.

Greatest Common Factor of 1966,6131

To find the highest common factor of 1966,6131, we have to find the factors of both numbers and list the highest common factor.

The factors of 1966 are 1, 2, 983, 1966

The factors of 6131 are 1, 6131

The HCF of 1966,6131 is 1.

Lets's calculate GCF of 1966,6131

Greatest Common Factor (GCF) of 1966,6131 By Common Division

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

Greatest Common Factor of 1966,6131 By Matching Biggest Common Factor Method

Now, list down the factors of 1966

1,2,983,1966

Now, list down the factors of 6131

1,6131

Greatest Common Factor

We found the factors 1966,6131 . The biggest common factor number is the GCF number.
So the greatest common factor 1966,6131 is 1.

Lets's calculate LCM of 106,7802

Lowest Common Multiple of 106,7802 using Common Division

2	106, 7802
	53, 3901

∴ So the LCM of the given numbers is 2 x 53 x 3901 = 413506

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/413506

Therefore, the GCF of Fractions 1966/106,6131/7802 is 1/413506

Least Common Multiple of 106,7802 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 106,7802 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(106,7802) = 2

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

GCF(106,7802) x common factors =2 x 1 = 2

LCM(106,7802) = ( 106 × 7802 ) / 2

LCM(106,7802) = 827012 / 2

LCM(106,7802) = 413506

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FAQs on GCF of Fractions of 1966/106, 6131/7802

1. What is the HCF of 1966,6131?

The HCF of 1966,6131 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 1966/106, 6131/7802?

Answer: GCF of Numerators as per given numbers 1966/106, 6131/7802 is

GCF of Numerators i.e. for 1966,6131 is 1

LCM of denominators i.e. for 106,7802 is 413506.

Thus, GCF of Fractions is 1/413506.Finally, GCF of Fractions for 1966/106, 6131/7802 is 1/413506.