How to Find GCF of 324/59, 576/594?

GCF of 324/59, 576/594

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 324/59, 576/594 i.e 36/35046 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/59, 576/594.

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 324/59,576/594?

Given fractions are 324/59,576/594

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 324/59,576/594, numerators are 324,576

Denominators are 59,594

The GCF of 324,576 is 36 .

LCM of 59,594 is 35046.

The greatest common factor of 324/59,576/594 = [GCF of 324,576]/[LCM of 59,594]= 36/35046

Therefore, the GCF of 324/59,576/594 is 36/35046.

Greatest Common Factor of 324,576

To find the highest common factor of 324,576, we have to find the factors of both numbers and list the highest common factor.

The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324

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

The HCF of 324,576 is 36.

Lets's calculate GCF of 324,576

Greatest Common Factor (GCF) of 324,576 By Common Division

2	324, 576
2	162, 288
3	81, 144
3	27, 48
	9, 16

∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36

Greatest Common Factor of 324,576 By Matching Biggest Common Factor Method

Now, list down the factors of 324

1,2,3,4,6,9,12,18,27,36,54,81,108,162,324

Now, list down the factors of 576

1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576

Greatest Common Factor

We found the factors 324,576 . The biggest common factor number is the GCF number.
So the greatest common factor 324,576 is 36.

Lets's calculate LCM of 59,594

Lowest Common Multiple of 59,594 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 35046

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/35046

Therefore, the GCF of Fractions 324/59,576/594 is 36/35046

Least Common Multiple of 59,594 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 59,594 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(59,594) = 1

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

GCF(59,594) x common factors =1 x 1 = 1

LCM(59,594) = ( 59 × 594 ) / 1

LCM(59,594) = 35046 / 1

LCM(59,594) = 35046

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FAQs on GCF of Fractions of 324/59, 576/594

1. What is the HCF of 324,576?

The HCF of 324,576 is 36

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 324/59, 576/594?

Answer: GCF of Numerators as per given numbers 324/59, 576/594 is

GCF of Numerators i.e. for 324,576 is 36

LCM of denominators i.e. for 59,594 is 35046.

Thus, GCF of Fractions is 36/35046.Finally, GCF of Fractions for 324/59, 576/594 is 36/35046.