How to Find GCF of 2098/205, 4624/1559?

GCF of 2098/205, 4624/1559

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 2098/205, 4624/1559 i.e 2/319595 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2098/205, 4624/1559.

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 2098/205,4624/1559?

Given fractions are 2098/205,4624/1559

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 2098/205,4624/1559, numerators are 2098,4624

Denominators are 205,1559

The GCF of 2098,4624 is 2 .

LCM of 205,1559 is 319595.

The greatest common factor of 2098/205,4624/1559 = [GCF of 2098,4624]/[LCM of 205,1559]= 2/319595

Therefore, the GCF of 2098/205,4624/1559 is 2/319595.

Greatest Common Factor of 2098,4624

To find the highest common factor of 2098,4624, we have to find the factors of both numbers and list the highest common factor.

The factors of 2098 are 1, 2, 1049, 2098

The factors of 4624 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, 4624

The HCF of 2098,4624 is 2.

Lets's calculate GCF of 2098,4624

Greatest Common Factor (GCF) of 2098,4624 By Common Division

2	2098, 4624
	1049, 2312

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 2098,4624 By Matching Biggest Common Factor Method

Now, list down the factors of 2098

1,2,1049,2098

Now, list down the factors of 4624

1,2,4,8,16,17,34,68,136,272,289,578,1156,2312,4624

Greatest Common Factor

We found the factors 2098,4624 . The biggest common factor number is the GCF number.
So the greatest common factor 2098,4624 is 2.

Lets's calculate LCM of 205,1559

Lowest Common Multiple of 205,1559 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 319595

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/319595

Therefore, the GCF of Fractions 2098/205,4624/1559 is 2/319595

Least Common Multiple of 205,1559 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 205,1559 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(205,1559) = 1

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

GCF(205,1559) x common factors =1 x 1 = 1

LCM(205,1559) = ( 205 × 1559 ) / 1

LCM(205,1559) = 319595 / 1

LCM(205,1559) = 319595

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FAQs on GCF of Fractions of 2098/205, 4624/1559

1. What is the HCF of 2098,4624?

The HCF of 2098,4624 is 2

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 2098/205, 4624/1559?

Answer: GCF of Numerators as per given numbers 2098/205, 4624/1559 is

GCF of Numerators i.e. for 2098,4624 is 2

LCM of denominators i.e. for 205,1559 is 319595.

Thus, GCF of Fractions is 2/319595.Finally, GCF of Fractions for 2098/205, 4624/1559 is 2/319595.