How to Find GCF of 427/432, 768/592?

GCF of 427/432, 768/592

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 427/432, 768/592 i.e 1/15984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 427/432, 768/592.

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 427/432,768/592?

Given fractions are 427/432,768/592

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 427/432,768/592, numerators are 427,768

Denominators are 432,592

The GCF of 427,768 is 1 .

LCM of 432,592 is 15984.

The greatest common factor of 427/432,768/592 = [GCF of 427,768]/[LCM of 432,592]= 1/15984

Therefore, the GCF of 427/432,768/592 is 1/15984.

Greatest Common Factor of 427,768

To find the highest common factor of 427,768, we have to find the factors of both numbers and list the highest common factor.

The factors of 427 are 1, 7, 61, 427

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

The HCF of 427,768 is 1.

Lets's calculate GCF of 427,768

Greatest Common Factor (GCF) of 427,768 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 427,768 By Matching Biggest Common Factor Method

Now, list down the factors of 427

1,7,61,427

Now, list down the factors of 768

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Greatest Common Factor

We found the factors 427,768 . The biggest common factor number is the GCF number.
So the greatest common factor 427,768 is 1.

Lets's calculate LCM of 432,592

Lowest Common Multiple of 432,592 using Common Division

2	432, 592
2	216, 296
2	108, 148
2	54, 74
	27, 37

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 27 x 37 = 15984

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15984

Therefore, the GCF of Fractions 427/432,768/592 is 1/15984

Least Common Multiple of 432,592 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 432,592 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(432,592) = 16

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

GCF(432,592) x common factors =16 x 1 = 16

LCM(432,592) = ( 432 × 592 ) / 16

LCM(432,592) = 255744 / 16

LCM(432,592) = 15984

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FAQs on GCF of Fractions of 427/432, 768/592

1. What is the HCF of 427,768?

The HCF of 427,768 is 1

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 427/432, 768/592?

Answer: GCF of Numerators as per given numbers 427/432, 768/592 is

GCF of Numerators i.e. for 427,768 is 1

LCM of denominators i.e. for 432,592 is 15984.

Thus, GCF of Fractions is 1/15984.Finally, GCF of Fractions for 427/432, 768/592 is 1/15984.