Get help with finding GCF of fractions 12/12, 30/30, 144/72 using GCF of Fractions Calculator to know the result 6/360 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 12/12, 30/30, 144/72 is **6/360**.

GCF(12/12, 30/30, 144/72) = 6/360

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

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

Given fractions are 12/12,30/30,144/72

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 12,30,144

Greatest Common Factor of Numerators i.e. GCF of 12,30,144 is 6 .

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

LCM of 12,30,72 is 360 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 12,30,144

2 | 12, 30, 144 |

3 | 6, 15, 72 |

2, 5, 24 |

∴ So the GCF of the given numbers is 2 x 3 = 6

**Factors of 12**

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

1,2,3,4,6,12

**Factors of 30**

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

**Factors of 144**

List of positive integer factors of 144 that divides 144 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

**Greatest Common Factor**

We found the factors 12,30,144 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 12,30,144 ** is **6**.

Lets's calculate LCM of 12,30,72

2 | 12, 30, 72 |

2 | 6, 15, 36 |

3 | 3, 15, 18 |

1, 5, 6 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 5 x 6 = 360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/360

Therefore, the GCF of Fractions 12/12,30/30,144/72 is 6/360

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 12,30,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,30,72) = 6

common factors(in case of two or more numbers have common factors) = 12

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

LCM(12,30,72) = ( 12 × 30 × 72 ) / 72

LCM(12,30,72) = 25920 / 72

LCM(12,30,72) = 360

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 12/12, 30/30, 144/72?

Answer: GCF of Numerators as per given numbers 12/12, 30/30, 144/72 is

GCF of Numerators i.e. for 12,30,144 is 6

LCM of denominators i.e. for 12,30,72 is 360.

Thus, GCF of Fractions is 6/360.Finally, GCF of Fractions for 12/12, 30/30, 144/72 is 6/360.