How to Find GCF of 171/76, 399/2912?

GCF of 171/76, 399/2912

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 171/76, 399/2912 i.e 57/55328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 171/76, 399/2912.

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 171/76,399/2912?

Given fractions are 171/76,399/2912

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 171/76,399/2912, numerators are 171,399

Denominators are 76,2912

The GCF of 171,399 is 57 .

LCM of 76,2912 is 55328.

The greatest common factor of 171/76,399/2912 = [GCF of 171,399]/[LCM of 76,2912]= 57/55328

Therefore, the GCF of 171/76,399/2912 is 57/55328.

Greatest Common Factor of 171,399

To find the highest common factor of 171,399, we have to find the factors of both numbers and list the highest common factor.

The factors of 171 are 1, 3, 9, 19, 57, 171

The factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399

The HCF of 171,399 is 57.

Lets's calculate GCF of 171,399

Greatest Common Factor (GCF) of 171,399 By Common Division

3	171, 399
19	57, 133
	3, 7

∴ So the GCF of the given numbers is 3 x 19 = 57

Greatest Common Factor of 171,399 By Matching Biggest Common Factor Method

Now, list down the factors of 171

1,3,9,19,57,171

Now, list down the factors of 399

1,3,7,19,21,57,133,399

Greatest Common Factor

We found the factors 171,399 . The biggest common factor number is the GCF number.
So the greatest common factor 171,399 is 57.

Lets's calculate LCM of 76,2912

Lowest Common Multiple of 76,2912 using Common Division

2	76, 2912
2	38, 1456
	19, 728

∴ So the LCM of the given numbers is 2 x 2 x 19 x 728 = 55328

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 57/55328

Therefore, the GCF of Fractions 171/76,399/2912 is 57/55328

Least Common Multiple of 76,2912 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 76,2912 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,2912) = 4

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

GCF(76,2912) x common factors =4 x 1 = 4

LCM(76,2912) = ( 76 × 2912 ) / 4

LCM(76,2912) = 221312 / 4

LCM(76,2912) = 55328

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 171/76, 399/2912

1. What is the HCF of 171,399?

The HCF of 171,399 is 57

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 171/76, 399/2912?

Answer: GCF of Numerators as per given numbers 171/76, 399/2912 is

GCF of Numerators i.e. for 171,399 is 57

LCM of denominators i.e. for 76,2912 is 55328.

Thus, GCF of Fractions is 57/55328.Finally, GCF of Fractions for 171/76, 399/2912 is 57/55328.