How to Find GCF of 798/410, 3109/404?

GCF of 798/410, 3109/404

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 798/410, 3109/404 i.e 1/82820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 798/410, 3109/404.

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 798/410,3109/404?

Given fractions are 798/410,3109/404

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 798/410,3109/404, numerators are 798,3109

Denominators are 410,404

The GCF of 798,3109 is 1 .

LCM of 410,404 is 82820.

The greatest common factor of 798/410,3109/404 = [GCF of 798,3109]/[LCM of 410,404]= 1/82820

Therefore, the GCF of 798/410,3109/404 is 1/82820.

Greatest Common Factor of 798,3109

To find the highest common factor of 798,3109, we have to find the factors of both numbers and list the highest common factor.

The factors of 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798

The factors of 3109 are 1, 3109

The HCF of 798,3109 is 1.

Lets's calculate GCF of 798,3109

Greatest Common Factor (GCF) of 798,3109 By Common Division

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

Greatest Common Factor of 798,3109 By Matching Biggest Common Factor Method

Now, list down the factors of 798

1,2,3,6,7,14,19,21,38,42,57,114,133,266,399,798

Now, list down the factors of 3109

1,3109

Greatest Common Factor

We found the factors 798,3109 . The biggest common factor number is the GCF number.
So the greatest common factor 798,3109 is 1.

Lets's calculate LCM of 410,404

Lowest Common Multiple of 410,404 using Common Division

2	410, 404
	205, 202

∴ So the LCM of the given numbers is 2 x 205 x 202 = 82820

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82820

Therefore, the GCF of Fractions 798/410,3109/404 is 1/82820

Least Common Multiple of 410,404 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 410,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(410,404) = 2

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

GCF(410,404) x common factors =2 x 1 = 2

LCM(410,404) = ( 410 × 404 ) / 2

LCM(410,404) = 165640 / 2

LCM(410,404) = 82820

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FAQs on GCF of Fractions of 798/410, 3109/404

1. What is the HCF of 798,3109?

The HCF of 798,3109 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 798/410, 3109/404?

Answer: GCF of Numerators as per given numbers 798/410, 3109/404 is

GCF of Numerators i.e. for 798,3109 is 1

LCM of denominators i.e. for 410,404 is 82820.

Thus, GCF of Fractions is 1/82820.Finally, GCF of Fractions for 798/410, 3109/404 is 1/82820.