How to Find GCF of 1266/218, 6619/8314?

GCF of 1266/218, 6619/8314

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 1266/218, 6619/8314 i.e 1/906226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1266/218, 6619/8314.

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 1266/218,6619/8314?

Given fractions are 1266/218,6619/8314

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 1266/218,6619/8314, numerators are 1266,6619

Denominators are 218,8314

The GCF of 1266,6619 is 1 .

LCM of 218,8314 is 906226.

The greatest common factor of 1266/218,6619/8314 = [GCF of 1266,6619]/[LCM of 218,8314]= 1/906226

Therefore, the GCF of 1266/218,6619/8314 is 1/906226.

Greatest Common Factor of 1266,6619

To find the highest common factor of 1266,6619, we have to find the factors of both numbers and list the highest common factor.

The factors of 1266 are 1, 2, 3, 6, 211, 422, 633, 1266

The factors of 6619 are 1, 6619

The HCF of 1266,6619 is 1.

Lets's calculate GCF of 1266,6619

Greatest Common Factor (GCF) of 1266,6619 By Common Division

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

Greatest Common Factor of 1266,6619 By Matching Biggest Common Factor Method

Now, list down the factors of 1266

1,2,3,6,211,422,633,1266

Now, list down the factors of 6619

1,6619

Greatest Common Factor

We found the factors 1266,6619 . The biggest common factor number is the GCF number.
So the greatest common factor 1266,6619 is 1.

Lets's calculate LCM of 218,8314

Lowest Common Multiple of 218,8314 using Common Division

2	218, 8314
	109, 4157

∴ So the LCM of the given numbers is 2 x 109 x 4157 = 906226

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/906226

Therefore, the GCF of Fractions 1266/218,6619/8314 is 1/906226

Least Common Multiple of 218,8314 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 218,8314 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(218,8314) = 2

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

GCF(218,8314) x common factors =2 x 1 = 2

LCM(218,8314) = ( 218 × 8314 ) / 2

LCM(218,8314) = 1812452 / 2

LCM(218,8314) = 906226

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FAQs on GCF of Fractions of 1266/218, 6619/8314

1. What is the HCF of 1266,6619?

The HCF of 1266,6619 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 1266/218, 6619/8314?

Answer: GCF of Numerators as per given numbers 1266/218, 6619/8314 is

GCF of Numerators i.e. for 1266,6619 is 1

LCM of denominators i.e. for 218,8314 is 906226.

Thus, GCF of Fractions is 1/906226.Finally, GCF of Fractions for 1266/218, 6619/8314 is 1/906226.