How to Find GCF of 324/480, 276/576?

GCF of 324/480, 276/576

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 324/480, 276/576 i.e 12/2880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/480, 276/576.

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 324/480,276/576?

Given fractions are 324/480,276/576

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 324/480,276/576, numerators are 324,276

Denominators are 480,576

The GCF of 324,276 is 12 .

LCM of 480,576 is 2880.

The greatest common factor of 324/480,276/576 = [GCF of 324,276]/[LCM of 480,576]= 12/2880

Therefore, the GCF of 324/480,276/576 is 12/2880.

Greatest Common Factor of 324,276

To find the highest common factor of 324,276, 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 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276

The HCF of 324,276 is 12.

Lets's calculate GCF of 324,276

Greatest Common Factor (GCF) of 324,276 By Common Division

2	324, 276
2	162, 138
3	81, 69
	27, 23

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 324,276 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 276

1,2,3,4,6,12,23,46,69,92,138,276

Greatest Common Factor

We found the factors 324,276 . The biggest common factor number is the GCF number.
So the greatest common factor 324,276 is 12.

Lets's calculate LCM of 480,576

Lowest Common Multiple of 480,576 using Common Division

2	480, 576
2	240, 288
2	120, 144
2	60, 72
2	30, 36
3	15, 18
	5, 6

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 6 = 2880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/2880

Therefore, the GCF of Fractions 324/480,276/576 is 12/2880

Least Common Multiple of 480,576 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 480,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(480,576) = 96

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

GCF(480,576) x common factors =96 x 1 = 96

LCM(480,576) = ( 480 × 576 ) / 96

LCM(480,576) = 276480 / 96

LCM(480,576) = 2880

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FAQs on GCF of Fractions of 324/480, 276/576

1. What is the HCF of 324,276?

The HCF of 324,276 is 12

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 324/480, 276/576?

Answer: GCF of Numerators as per given numbers 324/480, 276/576 is

GCF of Numerators i.e. for 324,276 is 12

LCM of denominators i.e. for 480,576 is 2880.

Thus, GCF of Fractions is 12/2880.Finally, GCF of Fractions for 324/480, 276/576 is 12/2880.