How to Find GCF of 384/509, 364/325?

GCF of 384/509, 364/325

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 384/509, 364/325 i.e 4/165425 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/509, 364/325.

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 384/509,364/325?

Given fractions are 384/509,364/325

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 384/509,364/325, numerators are 384,364

Denominators are 509,325

The GCF of 384,364 is 4 .

LCM of 509,325 is 165425.

The greatest common factor of 384/509,364/325 = [GCF of 384,364]/[LCM of 509,325]= 4/165425

Therefore, the GCF of 384/509,364/325 is 4/165425.

Greatest Common Factor of 384,364

To find the highest common factor of 384,364, we have to find the factors of both numbers and list the highest common factor.

The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

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

The HCF of 384,364 is 4.

Lets's calculate GCF of 384,364

Greatest Common Factor (GCF) of 384,364 By Common Division

2	384, 364
2	192, 182
	96, 91

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

Greatest Common Factor of 384,364 By Matching Biggest Common Factor Method

Now, list down the factors of 384

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384

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 384,364 . The biggest common factor number is the GCF number.
So the greatest common factor 384,364 is 4.

Lets's calculate LCM of 509,325

Lowest Common Multiple of 509,325 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 165425

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/165425

Therefore, the GCF of Fractions 384/509,364/325 is 4/165425

Least Common Multiple of 509,325 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 509,325 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(509,325) = 1

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

GCF(509,325) x common factors =1 x 1 = 1

LCM(509,325) = ( 509 × 325 ) / 1

LCM(509,325) = 165425 / 1

LCM(509,325) = 165425

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 384/509, 364/325

1. What is the HCF of 384,364?

The HCF of 384,364 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 384/509, 364/325?

Answer: GCF of Numerators as per given numbers 384/509, 364/325 is

GCF of Numerators i.e. for 384,364 is 4

LCM of denominators i.e. for 509,325 is 165425.

Thus, GCF of Fractions is 4/165425.Finally, GCF of Fractions for 384/509, 364/325 is 4/165425.