How to Find GCF of 588/47, 784/6753?

GCF of 588/47, 784/6753

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 588/47, 784/6753 i.e 196/317391 easily. The following is the detailed procedure to determine the greatest common factor of fractions 588/47, 784/6753.

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 588/47,784/6753?

Given fractions are 588/47,784/6753

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 588/47,784/6753, numerators are 588,784

Denominators are 47,6753

The GCF of 588,784 is 196 .

LCM of 47,6753 is 317391.

The greatest common factor of 588/47,784/6753 = [GCF of 588,784]/[LCM of 47,6753]= 196/317391

Therefore, the GCF of 588/47,784/6753 is 196/317391.

Greatest Common Factor of 588,784

To find the highest common factor of 588,784, we have to find the factors of both numbers and list the highest common factor.

The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The HCF of 588,784 is 196.

Lets's calculate GCF of 588,784

Greatest Common Factor (GCF) of 588,784 By Common Division

2	588, 784
2	294, 392
7	147, 196
7	21, 28
	3, 4

∴ So the GCF of the given numbers is 2 x 2 x 7 x 7 = 196

Greatest Common Factor of 588,784 By Matching Biggest Common Factor Method

Now, list down the factors of 588

1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588

Now, list down the factors of 784

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Greatest Common Factor

We found the factors 588,784 . The biggest common factor number is the GCF number.
So the greatest common factor 588,784 is 196.

Lets's calculate LCM of 47,6753

Lowest Common Multiple of 47,6753 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 317391

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 196/317391

Therefore, the GCF of Fractions 588/47,784/6753 is 196/317391

Least Common Multiple of 47,6753 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 47,6753 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(47,6753) = 1

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

GCF(47,6753) x common factors =1 x 1 = 1

LCM(47,6753) = ( 47 × 6753 ) / 1

LCM(47,6753) = 317391 / 1

LCM(47,6753) = 317391

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 588/47, 784/6753

1. What is the HCF of 588,784?

The HCF of 588,784 is 196

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 588/47, 784/6753?

Answer: GCF of Numerators as per given numbers 588/47, 784/6753 is

GCF of Numerators i.e. for 588,784 is 196

LCM of denominators i.e. for 47,6753 is 317391.

Thus, GCF of Fractions is 196/317391.Finally, GCF of Fractions for 588/47, 784/6753 is 196/317391.