How to Find GCF of 2284/249, 2304/200?

GCF of 2284/249, 2304/200

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 2284/249, 2304/200 i.e 4/49800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2284/249, 2304/200.

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 2284/249,2304/200?

Given fractions are 2284/249,2304/200

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 2284/249,2304/200, numerators are 2284,2304

Denominators are 249,200

The GCF of 2284,2304 is 4 .

LCM of 249,200 is 49800.

The greatest common factor of 2284/249,2304/200 = [GCF of 2284,2304]/[LCM of 249,200]= 4/49800

Therefore, the GCF of 2284/249,2304/200 is 4/49800.

Greatest Common Factor of 2284,2304

To find the highest common factor of 2284,2304, we have to find the factors of both numbers and list the highest common factor.

The factors of 2284 are 1, 2, 4, 571, 1142, 2284

The factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152, 2304

The HCF of 2284,2304 is 4.

Lets's calculate GCF of 2284,2304

Greatest Common Factor (GCF) of 2284,2304 By Common Division

2	2284, 2304
2	1142, 1152
	571, 576

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

Greatest Common Factor of 2284,2304 By Matching Biggest Common Factor Method

Now, list down the factors of 2284

1,2,4,571,1142,2284

Now, list down the factors of 2304

1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,128,144,192,256,288,384,576,768,1152,2304

Greatest Common Factor

We found the factors 2284,2304 . The biggest common factor number is the GCF number.
So the greatest common factor 2284,2304 is 4.

Lets's calculate LCM of 249,200

Lowest Common Multiple of 249,200 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 49800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/49800

Therefore, the GCF of Fractions 2284/249,2304/200 is 4/49800

Least Common Multiple of 249,200 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 249,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(249,200) = 1

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

GCF(249,200) x common factors =1 x 1 = 1

LCM(249,200) = ( 249 × 200 ) / 1

LCM(249,200) = 49800 / 1

LCM(249,200) = 49800

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FAQs on GCF of Fractions of 2284/249, 2304/200

1. What is the HCF of 2284,2304?

The HCF of 2284,2304 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 2284/249, 2304/200?

Answer: GCF of Numerators as per given numbers 2284/249, 2304/200 is

GCF of Numerators i.e. for 2284,2304 is 4

LCM of denominators i.e. for 249,200 is 49800.

Thus, GCF of Fractions is 4/49800.Finally, GCF of Fractions for 2284/249, 2304/200 is 4/49800.