Get help with finding GCF of fractions 45/180, 75/225, 100/270 using GCF of Fractions Calculator to know the result 5/2700 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 45/180, 75/225, 100/270 is **5/2700**.

GCF(45/180, 75/225, 100/270) = 5/2700

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

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

Given fractions are 45/180,75/225,100/270

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 45,75,100

Greatest Common Factor of Numerators i.e. GCF of 45,75,100 is 5 .

LCM of Denominators means LCM of 180,225,270 as per the given fractions.

LCM of 180,225,270 is 2700 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 45,75,100

5 | 45, 75, 100 |

9, 15, 20 |

∴ So the GCF of the given numbers is 5 = 5

**Factors of 45**

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

**Factors of 75**

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

**Factors of 100**

List of positive integer factors of 100 that divides 100 without a remainder.

1,2,4,5,10,20,25,50,100

**Greatest Common Factor**

We found the factors 45,75,100 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 45,75,100 ** is **5**.

Lets's calculate LCM of 180,225,270

2 | 180, 225, 270 |

3 | 90, 225, 135 |

3 | 30, 75, 45 |

5 | 10, 25, 15 |

2, 5, 3 |

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 2 x 5 x 3 = 2700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/2700

Therefore, the GCF of Fractions 45/180,75/225,100/270 is 5/2700

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 180,225,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(180,225,270) = 45

common factors(in case of two or more numbers have common factors) = 90

GCF(180,225,270) x common factors =45 x 90 = 4050

LCM(180,225,270) = ( 180 × 225 × 270 ) / 4050

LCM(180,225,270) = 10935000 / 4050

LCM(180,225,270) = 2700

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 45/180, 75/225, 100/270?

Answer: GCF of Numerators as per given numbers 45/180, 75/225, 100/270 is

GCF of Numerators i.e. for 45,75,100 is 5

LCM of denominators i.e. for 180,225,270 is 2700.

Thus, GCF of Fractions is 5/2700.Finally, GCF of Fractions for 45/180, 75/225, 100/270 is 5/2700.