How to Find GCF of 109/418, 5341/7002?

GCF of 109/418, 5341/7002

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 109/418, 5341/7002 i.e 109/1463418 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/418, 5341/7002.

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 109/418,5341/7002?

Given fractions are 109/418,5341/7002

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 109/418,5341/7002, numerators are 109,5341

Denominators are 418,7002

The GCF of 109,5341 is 109 .

LCM of 418,7002 is 1463418.

The greatest common factor of 109/418,5341/7002 = [GCF of 109,5341]/[LCM of 418,7002]= 109/1463418

Therefore, the GCF of 109/418,5341/7002 is 109/1463418.

Greatest Common Factor of 109,5341

To find the highest common factor of 109,5341, we have to find the factors of both numbers and list the highest common factor.

The factors of 109 are 1, 109

The factors of 5341 are 1, 7, 49, 109, 763, 5341

The HCF of 109,5341 is 109.

Lets's calculate GCF of 109,5341

Greatest Common Factor (GCF) of 109,5341 By Common Division

109	109, 5341
	1, 49

∴ So the GCF of the given numbers is 109 = 109

Greatest Common Factor of 109,5341 By Matching Biggest Common Factor Method

Now, list down the factors of 109

1,109

Now, list down the factors of 5341

1,7,49,109,763,5341

Greatest Common Factor

We found the factors 109,5341 . The biggest common factor number is the GCF number.
So the greatest common factor 109,5341 is 109.

Lets's calculate LCM of 418,7002

Lowest Common Multiple of 418,7002 using Common Division

2	418, 7002
	209, 3501

∴ So the LCM of the given numbers is 2 x 209 x 3501 = 1463418

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 109/1463418

Therefore, the GCF of Fractions 109/418,5341/7002 is 109/1463418

Least Common Multiple of 418,7002 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 418,7002 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(418,7002) = 2

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

GCF(418,7002) x common factors =2 x 1 = 2

LCM(418,7002) = ( 418 × 7002 ) / 2

LCM(418,7002) = 2926836 / 2

LCM(418,7002) = 1463418

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FAQs on GCF of Fractions of 109/418, 5341/7002

1. What is the HCF of 109,5341?

The HCF of 109,5341 is 109

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 109/418, 5341/7002?

Answer: GCF of Numerators as per given numbers 109/418, 5341/7002 is

GCF of Numerators i.e. for 109,5341 is 109

LCM of denominators i.e. for 418,7002 is 1463418.

Thus, GCF of Fractions is 109/1463418.Finally, GCF of Fractions for 109/418, 5341/7002 is 109/1463418.