Get help with finding GCF of fractions 7/12, 9/30, 14/42, 19/72 using GCF of Fractions Calculator to know the result 1/2520 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 7/12, 9/30, 14/42, 19/72 is **1/2520**.

GCF(7/12, 9/30, 14/42, 19/72) = 1/2520

Enter two or more fractions separated by **"commas"**

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

Given fractions are 7/12,9/30,14/42,19/72

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 7,9,14,19

Greatest Common Factor of Numerators i.e. GCF of 7,9,14,19 is 1 .

LCM of Denominators means LCM of 12,30,42,72 as per the given fractions.

LCM of 12,30,42,72 is 2520 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 7,9,14,19

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

**Factors of 7**

List of positive integer factors of 7 that divides 7 without a remainder.

1,7

**Factors of 9**

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

1,3,9

**Factors of 14**

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

1,2,7,14

**Factors of 19**

List of positive integer factors of 19 that divides 19 without a remainder.

1,19

**Greatest Common Factor**

We found the factors 7,9,14,19 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 7,9,14,19 ** is **1**.

Lets's calculate LCM of 12,30,42,72

2 | 12, 30, 42, 72 |

2 | 6, 15, 21, 36 |

3 | 3, 15, 21, 18 |

1, 5, 7, 6 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 5 x 7 x 6 = 2520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2520

Therefore, the GCF of Fractions 7/12,9/30,14/42,19/72 is 1/2520

The formula of **LCM** is LCM(a_{1},a_{2},a_{3}....,a_{n}) = ( a_{1} × a_{2} × a_{3} × .... × a_{n}) / GCF(a_{1},a_{2},a_{3}....,a_{n}) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 12,30,42,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,30,42,72) = 6

common factors(in case of two or more numbers have common factors) = 72

GCF(12,30,42,72) x common factors =6 x 72 = 432

LCM(12,30,42,72) = ( 12 × 30 × 42 × 72 ) / 432

LCM(12,30,42,72) = 1088640 / 432

LCM(12,30,42,72) = 2520

Here are some samples of GCF of Fractions calculations.

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 7/12, 9/30, 14/42, 19/72?

Answer: GCF of Numerators as per given numbers 7/12, 9/30, 14/42, 19/72 is

GCF of Numerators i.e. for 7,9,14,19 is 1

LCM of denominators i.e. for 12,30,42,72 is 2520.

Thus, GCF of Fractions is 1/2520.Finally, GCF of Fractions for 7/12, 9/30, 14/42, 19/72 is 1/2520.