How to Find GCF of 728/200, 364/684?

GCF of 728/200, 364/684

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 728/200, 364/684 i.e 364/34200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/200, 364/684.

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 728/200,364/684?

Given fractions are 728/200,364/684

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 728/200,364/684, numerators are 728,364

Denominators are 200,684

The GCF of 728,364 is 364 .

LCM of 200,684 is 34200.

The greatest common factor of 728/200,364/684 = [GCF of 728,364]/[LCM of 200,684]= 364/34200

Therefore, the GCF of 728/200,364/684 is 364/34200.

Greatest Common Factor of 728,364

To find the highest common factor of 728,364, we have to find the factors of both numbers and list the highest common factor.

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

The HCF of 728,364 is 364.

Lets's calculate GCF of 728,364

Greatest Common Factor (GCF) of 728,364 By Common Division

2	728, 364
2	364, 182
7	91, 182
13	13, 26
	1, 2

∴ So the GCF of the given numbers is 2 x 2 x 7 x 13 = 364

Greatest Common Factor of 728,364 By Matching Biggest Common Factor Method

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Now, list down the factors of 364

1,2,4,7,13,14,26,28,52,91,182,364

Greatest Common Factor

We found the factors 728,364 . The biggest common factor number is the GCF number.
So the greatest common factor 728,364 is 364.

Lets's calculate LCM of 200,684

Lowest Common Multiple of 200,684 using Common Division

2	200, 684
2	100, 342
	50, 171

∴ So the LCM of the given numbers is 2 x 2 x 50 x 171 = 34200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 364/34200

Therefore, the GCF of Fractions 728/200,364/684 is 364/34200

Least Common Multiple of 200,684 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 200,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(200,684) = 4

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

GCF(200,684) x common factors =4 x 1 = 4

LCM(200,684) = ( 200 × 684 ) / 4

LCM(200,684) = 136800 / 4

LCM(200,684) = 34200

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 728/200, 364/684

1. What is the HCF of 728,364?

The HCF of 728,364 is 364

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 728/200, 364/684?

Answer: GCF of Numerators as per given numbers 728/200, 364/684 is

GCF of Numerators i.e. for 728,364 is 364

LCM of denominators i.e. for 200,684 is 34200.

Thus, GCF of Fractions is 364/34200.Finally, GCF of Fractions for 728/200, 364/684 is 364/34200.