Get help with finding GCF of fractions 72/36, 180/45, 252/60 using GCF of Fractions Calculator to know the result 36/180 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 72/36, 180/45, 252/60 is **36/180**.

GCF(72/36, 180/45, 252/60) = 36/180

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

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

Given fractions are 72/36,180/45,252/60

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 72,180,252

Greatest Common Factor of Numerators i.e. GCF of 72,180,252 is 36 .

LCM of Denominators means LCM of 36,45,60 as per the given fractions.

LCM of 36,45,60 is 180 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 72,180,252

2 | 72, 180, 252 |

2 | 36, 90, 126 |

3 | 18, 45, 63 |

3 | 6, 15, 21 |

2, 5, 7 |

∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36

**Factors of 72**

List of positive integer factors of 72 that divides 72 without a remainder.

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

**Factors of 180**

List of positive integer factors of 180 that divides 180 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

**Factors of 252**

List of positive integer factors of 252 that divides 252 without a remainder.

1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252

**Greatest Common Factor**

We found the factors 72,180,252 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 72,180,252 ** is **36**.

Lets's calculate LCM of 36,45,60

2 | 36, 45, 60 |

2 | 18, 45, 30 |

3 | 9, 45, 15 |

3 | 3, 5, 15 |

5 | 1, 5, 5 |

1, 1, 1 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 1 x 1 x 1 = 180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/180

Therefore, the GCF of Fractions 72/36,180/45,252/60 is 36/180

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 36,45,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,45,60) = 3

common factors(in case of two or more numbers have common factors) = 180

GCF(36,45,60) x common factors =3 x 180 = 540

LCM(36,45,60) = ( 36 × 45 × 60 ) / 540

LCM(36,45,60) = 97200 / 540

LCM(36,45,60) = 180

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 72/36, 180/45, 252/60?

Answer: GCF of Numerators as per given numbers 72/36, 180/45, 252/60 is

GCF of Numerators i.e. for 72,180,252 is 36

LCM of denominators i.e. for 36,45,60 is 180.

Thus, GCF of Fractions is 36/180.Finally, GCF of Fractions for 72/36, 180/45, 252/60 is 36/180.