How to Find GCF of 288/600, 6764/724?

GCF of 288/600, 6764/724

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 288/600, 6764/724 i.e 4/108600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/600, 6764/724.

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 288/600,6764/724?

Given fractions are 288/600,6764/724

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 288/600,6764/724, numerators are 288,6764

Denominators are 600,724

The GCF of 288,6764 is 4 .

LCM of 600,724 is 108600.

The greatest common factor of 288/600,6764/724 = [GCF of 288,6764]/[LCM of 600,724]= 4/108600

Therefore, the GCF of 288/600,6764/724 is 4/108600.

Greatest Common Factor of 288,6764

To find the highest common factor of 288,6764, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 6764 are 1, 2, 4, 19, 38, 76, 89, 178, 356, 1691, 3382, 6764

The HCF of 288,6764 is 4.

Lets's calculate GCF of 288,6764

Greatest Common Factor (GCF) of 288,6764 By Common Division

2	288, 6764
2	144, 3382
	72, 1691

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

Greatest Common Factor of 288,6764 By Matching Biggest Common Factor Method

Now, list down the factors of 288

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

Now, list down the factors of 6764

1,2,4,19,38,76,89,178,356,1691,3382,6764

Greatest Common Factor

We found the factors 288,6764 . The biggest common factor number is the GCF number.
So the greatest common factor 288,6764 is 4.

Lets's calculate LCM of 600,724

Lowest Common Multiple of 600,724 using Common Division

2	600, 724
2	300, 362
	150, 181

∴ So the LCM of the given numbers is 2 x 2 x 150 x 181 = 108600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/108600

Therefore, the GCF of Fractions 288/600,6764/724 is 4/108600

Least Common Multiple of 600,724 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 600,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(600,724) = 4

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

GCF(600,724) x common factors =4 x 1 = 4

LCM(600,724) = ( 600 × 724 ) / 4

LCM(600,724) = 434400 / 4

LCM(600,724) = 108600

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FAQs on GCF of Fractions of 288/600, 6764/724

1. What is the HCF of 288,6764?

The HCF of 288,6764 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 288/600, 6764/724?

Answer: GCF of Numerators as per given numbers 288/600, 6764/724 is

GCF of Numerators i.e. for 288,6764 is 4

LCM of denominators i.e. for 600,724 is 108600.

Thus, GCF of Fractions is 4/108600.Finally, GCF of Fractions for 288/600, 6764/724 is 4/108600.