Greatest Common Factor of 417/528, 312/458

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 417/528, 312/458

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 417/528,312/458

Given fractions are 417/528,312/458

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 417,312

Greatest Common Factor of Numerators i.e. GCF of 417,312 is 3 .

LCM of Denominators means LCM of 528,458 as per the given fractions.

LCM of 528,458 is 120912 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 417,312

GCF of Fractions 417/528,312/458 is 3/120912

3 417, 312
139, 104

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 417,312 By Matching Biggest Common Factor Method

Greatest Common Factor of 417,312 By Matching Biggest Common Factor Method

Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1,3,139,417

Factors of 312

List of positive integer factors of 312 that divides 312 without a remainder.

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 417,312 . The biggest common factor number is the GCF number.
So the greatest common factor 417,312 is 3.

Lets's calculate LCM of 528,458

2 528, 458
264, 229

∴ So the LCM of the given numbers is 2 x 264 x 229 = 120912

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/120912

Therefore, the GCF of Fractions 417/528,312/458 is 3/120912

Least Common Multiple of 528,458 with GCF Formula

Least Common Multiple of 528,458 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 528,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(528,458) = 2

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

GCF(528,458) x common factors =2 x 1 = 2

LCM(528,458) = ( 528 × 458 ) / 2

LCM(528,458) = 241824 / 2

LCM(528,458) = 120912


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 417/528, 312/458

1. 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.

2. What is the GCF of Fractions for 417/528, 312/458?

Answer: GCF of Numerators as per given numbers 417/528, 312/458 is

GCF of Numerators i.e. for 417,312 is 3

LCM of denominators i.e. for 528,458 is 120912.

Thus, GCF of Fractions is 3/120912.Finally, GCF of Fractions for 417/528, 312/458 is 3/120912.