Greatest Common Factor of 1/65, 8/17, 71/30, 24/312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 1/65, 8/17, 71/30, 24/312

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 1/65,8/17,71/30,24/312

Given fractions are 1/65,8/17,71/30,24/312

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 1,8,71,24

Greatest Common Factor of Numerators i.e. GCF of 1,8,71,24 is 1 .

LCM of Denominators means LCM of 65,17,30,312 as per the given fractions.

LCM of 65,17,30,312 is 26520 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 1,8,71,24

GCF of Fractions 1/65,8/17,71/30,24/312 is 1/26520

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

Greatest Common Factor of 1,8,71,24 By Matching Biggest Common Factor Method

Greatest Common Factor of 1,8,71,24 By Matching Biggest Common Factor Method

Factors of 1

List of positive integer factors of 1 that divides 1 without a remainder.

1

Factors of 8

List of positive integer factors of 8 that divides 8 without a remainder.

1,2,4,8

Factors of 71

List of positive integer factors of 71 that divides 71 without a remainder.

1,71

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1,2,3,4,6,8,12,24

Greatest Common Factor

We found the factors 1,8,71,24 . The biggest common factor number is the GCF number.
So the greatest common factor 1,8,71,24 is 1.

Lets's calculate LCM of 65,17,30,312

2 65, 17, 30, 312
3 65, 17, 15, 156
5 65, 17, 5, 52
13 13, 17, 1, 52
1, 17, 1, 4

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 1 x 17 x 1 x 4 = 26520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26520

Therefore, the GCF of Fractions 1/65,8/17,71/30,24/312 is 1/26520

Least Common Multiple of 65,17,30,312 with GCF Formula

Least Common Multiple of 65,17,30,312 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 65,17,30,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,17,30,312) = 1

common factors(in case of two or more numbers have common factors) = 390

GCF(65,17,30,312) x common factors =1 x 390 = 390

LCM(65,17,30,312) = ( 65 × 17 × 30 × 312 ) / 390

LCM(65,17,30,312) = 10342800 / 390

LCM(65,17,30,312) = 26520


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 1/65, 8/17, 71/30, 24/312

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 1/65, 8/17, 71/30, 24/312?

Answer: GCF of Numerators as per given numbers 1/65, 8/17, 71/30, 24/312 is

GCF of Numerators i.e. for 1,8,71,24 is 1

LCM of denominators i.e. for 65,17,30,312 is 26520.

Thus, GCF of Fractions is 1/26520.Finally, GCF of Fractions for 1/65, 8/17, 71/30, 24/312 is 1/26520.