How to Find GCF of 588/73, 364/172?

GCF of 588/73, 364/172

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 588/73, 364/172 i.e 28/12556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 588/73, 364/172.

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 588/73,364/172?

Given fractions are 588/73,364/172

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 588/73,364/172, numerators are 588,364

Denominators are 73,172

The GCF of 588,364 is 28 .

LCM of 73,172 is 12556.

The greatest common factor of 588/73,364/172 = [GCF of 588,364]/[LCM of 73,172]= 28/12556

Therefore, the GCF of 588/73,364/172 is 28/12556.

Greatest Common Factor of 588,364

To find the highest common factor of 588,364, 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 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

The HCF of 588,364 is 28.

Lets's calculate GCF of 588,364

Greatest Common Factor (GCF) of 588,364 By Common Division

2	588, 364
2	294, 182
7	147, 91
	21, 13

∴ So the GCF of the given numbers is 2 x 2 x 7 = 28

Greatest Common Factor of 588,364 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 364

1,2,4,7,13,14,26,28,52,91,182,364

Greatest Common Factor

We found the factors 588,364 . The biggest common factor number is the GCF number.
So the greatest common factor 588,364 is 28.

Lets's calculate LCM of 73,172

Lowest Common Multiple of 73,172 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 12556

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/12556

Therefore, the GCF of Fractions 588/73,364/172 is 28/12556

Least Common Multiple of 73,172 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 73,172 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(73,172) = 1

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

GCF(73,172) x common factors =1 x 1 = 1

LCM(73,172) = ( 73 × 172 ) / 1

LCM(73,172) = 12556 / 1

LCM(73,172) = 12556

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FAQs on GCF of Fractions of 588/73, 364/172

1. What is the HCF of 588,364?

The HCF of 588,364 is 28

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 588/73, 364/172?

Answer: GCF of Numerators as per given numbers 588/73, 364/172 is

GCF of Numerators i.e. for 588,364 is 28

LCM of denominators i.e. for 73,172 is 12556.

Thus, GCF of Fractions is 28/12556.Finally, GCF of Fractions for 588/73, 364/172 is 28/12556.