Greatest Common Factor of 16/30, 45/21, 12/49, 71/209

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 16/30, 45/21, 12/49, 71/209

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 16/30,45/21,12/49,71/209

Given fractions are 16/30,45/21,12/49,71/209

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 16,45,12,71

Greatest Common Factor of Numerators i.e. GCF of 16,45,12,71 is 1 .

LCM of Denominators means LCM of 30,21,49,209 as per the given fractions.

LCM of 30,21,49,209 is 307230 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 16,45,12,71

GCF of Fractions 16/30,45/21,12/49,71/209 is 1/307230

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

Greatest Common Factor of 16,45,12,71 By Matching Biggest Common Factor Method

Greatest Common Factor of 16,45,12,71 By Matching Biggest Common Factor Method

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 71

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

1,71

Greatest Common Factor

We found the factors 16,45,12,71 . The biggest common factor number is the GCF number.
So the greatest common factor 16,45,12,71 is 1.

Lets's calculate LCM of 30,21,49,209

3 30, 21, 49, 209
7 10, 7, 49, 209
10, 1, 7, 209

∴ So the LCM of the given numbers is 3 x 7 x 10 x 1 x 7 x 209 = 307230

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/307230

Therefore, the GCF of Fractions 16/30,45/21,12/49,71/209 is 1/307230

Least Common Multiple of 30,21,49,209 with GCF Formula

Least Common Multiple of 30,21,49,209 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 30,21,49,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,21,49,209) = 1

common factors(in case of two or more numbers have common factors) = 21

GCF(30,21,49,209) x common factors =1 x 21 = 21

LCM(30,21,49,209) = ( 30 × 21 × 49 × 209 ) / 21

LCM(30,21,49,209) = 6451830 / 21

LCM(30,21,49,209) = 307230


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 16/30, 45/21, 12/49, 71/209

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 16/30, 45/21, 12/49, 71/209?

Answer: GCF of Numerators as per given numbers 16/30, 45/21, 12/49, 71/209 is

GCF of Numerators i.e. for 16,45,12,71 is 1

LCM of denominators i.e. for 30,21,49,209 is 307230.

Thus, GCF of Fractions is 1/307230.Finally, GCF of Fractions for 16/30, 45/21, 12/49, 71/209 is 1/307230.