Greatest Common Factor of 9/46, 480/30, 414/75

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 9/46, 480/30, 414/75

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 9/46,480/30,414/75

Given fractions are 9/46,480/30,414/75

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 9,480,414

Greatest Common Factor of Numerators i.e. GCF of 9,480,414 is 3 .

LCM of Denominators means LCM of 46,30,75 as per the given fractions.

LCM of 46,30,75 is 3450 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 9,480,414

GCF of Fractions 9/46,480/30,414/75 is 3/3450

3 9, 480, 414
3, 160, 138

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

Greatest Common Factor of 9,480,414 By Matching Biggest Common Factor Method

Greatest Common Factor of 9,480,414 By Matching Biggest Common Factor Method

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1,3,9

Factors of 480

List of positive integer factors of 480 that divides 480 without a remainder.

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 9,480,414 . The biggest common factor number is the GCF number.
So the greatest common factor 9,480,414 is 3.

Lets's calculate LCM of 46,30,75

2 46, 30, 75
3 23, 15, 75
5 23, 5, 25
23, 1, 5

∴ So the LCM of the given numbers is 2 x 3 x 5 x 23 x 1 x 5 = 3450

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3450

Therefore, the GCF of Fractions 9/46,480/30,414/75 is 3/3450

Least Common Multiple of 46,30,75 with GCF Formula

Least Common Multiple of 46,30,75 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 46,30,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(46,30,75) = 1

common factors(in case of two or more numbers have common factors) = 30

GCF(46,30,75) x common factors =1 x 30 = 30

LCM(46,30,75) = ( 46 × 30 × 75 ) / 30

LCM(46,30,75) = 103500 / 30

LCM(46,30,75) = 3450


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 9/46, 480/30, 414/75

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 9/46, 480/30, 414/75?

Answer: GCF of Numerators as per given numbers 9/46, 480/30, 414/75 is

GCF of Numerators i.e. for 9,480,414 is 3

LCM of denominators i.e. for 46,30,75 is 3450.

Thus, GCF of Fractions is 3/3450.Finally, GCF of Fractions for 9/46, 480/30, 414/75 is 3/3450.