How to Find GCF of 2204/813, 1784/1519?

GCF of 2204/813, 1784/1519

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 2204/813, 1784/1519 i.e 4/1234947 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2204/813, 1784/1519.

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 2204/813,1784/1519?

Given fractions are 2204/813,1784/1519

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 2204/813,1784/1519, numerators are 2204,1784

Denominators are 813,1519

The GCF of 2204,1784 is 4 .

LCM of 813,1519 is 1234947.

The greatest common factor of 2204/813,1784/1519 = [GCF of 2204,1784]/[LCM of 813,1519]= 4/1234947

Therefore, the GCF of 2204/813,1784/1519 is 4/1234947.

Greatest Common Factor of 2204,1784

To find the highest common factor of 2204,1784, we have to find the factors of both numbers and list the highest common factor.

The factors of 2204 are 1, 2, 4, 19, 29, 38, 58, 76, 116, 551, 1102, 2204

The factors of 1784 are 1, 2, 4, 8, 223, 446, 892, 1784

The HCF of 2204,1784 is 4.

Lets's calculate GCF of 2204,1784

Greatest Common Factor (GCF) of 2204,1784 By Common Division

2	2204, 1784
2	1102, 892
	551, 446

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 2204,1784 By Matching Biggest Common Factor Method

Now, list down the factors of 2204

1,2,4,19,29,38,58,76,116,551,1102,2204

Now, list down the factors of 1784

1,2,4,8,223,446,892,1784

Greatest Common Factor

We found the factors 2204,1784 . The biggest common factor number is the GCF number.
So the greatest common factor 2204,1784 is 4.

Lets's calculate LCM of 813,1519

Lowest Common Multiple of 813,1519 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1234947

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1234947

Therefore, the GCF of Fractions 2204/813,1784/1519 is 4/1234947

Least Common Multiple of 813,1519 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 813,1519 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(813,1519) = 1

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

GCF(813,1519) x common factors =1 x 1 = 1

LCM(813,1519) = ( 813 × 1519 ) / 1

LCM(813,1519) = 1234947 / 1

LCM(813,1519) = 1234947

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 2204/813, 1784/1519

1. What is the HCF of 2204,1784?

The HCF of 2204,1784 is 4

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 2204/813, 1784/1519?

Answer: GCF of Numerators as per given numbers 2204/813, 1784/1519 is

GCF of Numerators i.e. for 2204,1784 is 4

LCM of denominators i.e. for 813,1519 is 1234947.

Thus, GCF of Fractions is 4/1234947.Finally, GCF of Fractions for 2204/813, 1784/1519 is 4/1234947.