# Greatest Common Factor of 6/75, 14/120, 15/200

Get help with finding GCF of fractions 6/75, 14/120, 15/200 using GCF of Fractions Calculator to know the result 1/600 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 6/75, 14/120, 15/200 is 1/600.

GCF(6/75, 14/120, 15/200) = 1/600

## GCF of 6/75, 14/120, 15/200

Enter two or more fractions separated by "commas"

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

GCF of:

Given fractions are 6/75,14/120,15/200

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 6,14,15

Greatest Common Factor of Numerators i.e. GCF of 6,14,15 is 1 .

LCM of Denominators means LCM of 75,120,200 as per the given fractions.

LCM of 75,120,200 is 600 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 6,14,15

### Greatest Common Factor (GCF) of 6,14,15 By Common Division

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

Greatest Common Factor of 6,14,15 By Matching Biggest Common Factor Method

### Greatest Common Factor of 6,14,15 By Matching Biggest Common Factor Method

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1,3,5,15

Greatest Common Factor

We found the factors 6,14,15 . The biggest common factor number is the GCF number.
So the greatest common factor 6,14,15 is 1.

Lets's calculate LCM of 75,120,200

### Least Common Multiple (LCM) of 75,120,200 By Common Division

 2 75, 120, 200 2 75, 60, 100 2 75, 30, 50 3 75, 15, 25 5 25, 5, 25 5 1, 5, 5 1, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 5 x 1 x 1 x 1 = 600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/600

Therefore, the GCF of Fractions 6/75,14/120,15/200 is 1/600

Least Common Multiple of 75,120,200 with GCF Formula

### Least Common Multiple of 75,120,200 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 75,120,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,120,200) = 5

common factors(in case of two or more numbers have common factors) = 600

GCF(75,120,200) x common factors =5 x 600 = 3000

LCM(75,120,200) = ( 75 × 120 × 200 ) / 3000

LCM(75,120,200) = 1800000 / 3000

LCM(75,120,200) = 600

### GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

### Frequently Asked Questions on Fractional GCF of 6/75, 14/120, 15/200

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 6/75, 14/120, 15/200?

Answer: GCF of Numerators as per given numbers 6/75, 14/120, 15/200 is

GCF of Numerators i.e. for 6,14,15 is 1

LCM of denominators i.e. for 75,120,200 is 600.

Thus, GCF of Fractions is 1/600.Finally, GCF of Fractions for 6/75, 14/120, 15/200 is 1/600.