How to Find GCF of 592/27, 512/7946?

GCF of 592/27, 512/7946

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 592/27, 512/7946 i.e 16/214542 easily. The following is the detailed procedure to determine the greatest common factor of fractions 592/27, 512/7946.

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 592/27,512/7946?

Given fractions are 592/27,512/7946

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 592/27,512/7946, numerators are 592,512

Denominators are 27,7946

The GCF of 592,512 is 16 .

LCM of 27,7946 is 214542.

The greatest common factor of 592/27,512/7946 = [GCF of 592,512]/[LCM of 27,7946]= 16/214542

Therefore, the GCF of 592/27,512/7946 is 16/214542.

Greatest Common Factor of 592,512

To find the highest common factor of 592,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 592,512 is 16.

Lets's calculate GCF of 592,512

Greatest Common Factor (GCF) of 592,512 By Common Division

2	592, 512
2	296, 256
2	148, 128
2	74, 64
	37, 32

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 592,512 By Matching Biggest Common Factor Method

Now, list down the factors of 592

1,2,4,8,16,37,74,148,296,592

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 592,512 . The biggest common factor number is the GCF number.
So the greatest common factor 592,512 is 16.

Lets's calculate LCM of 27,7946

Lowest Common Multiple of 27,7946 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 214542

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/214542

Therefore, the GCF of Fractions 592/27,512/7946 is 16/214542

Least Common Multiple of 27,7946 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 27,7946 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,7946) = 1

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

GCF(27,7946) x common factors =1 x 1 = 1

LCM(27,7946) = ( 27 × 7946 ) / 1

LCM(27,7946) = 214542 / 1

LCM(27,7946) = 214542

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FAQs on GCF of Fractions of 592/27, 512/7946

1. What is the HCF of 592,512?

The HCF of 592,512 is 16

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 592/27, 512/7946?

Answer: GCF of Numerators as per given numbers 592/27, 512/7946 is

GCF of Numerators i.e. for 592,512 is 16

LCM of denominators i.e. for 27,7946 is 214542.

Thus, GCF of Fractions is 16/214542.Finally, GCF of Fractions for 592/27, 512/7946 is 16/214542.