Get help with finding GCF of fractions 105/36, 150/54, 210/126 using GCF of Fractions Calculator to know the result 15/756 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 105/36, 150/54, 210/126 is **15/756**.

GCF(105/36, 150/54, 210/126) = 15/756

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

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

Given fractions are 105/36,150/54,210/126

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 105,150,210

Greatest Common Factor of Numerators i.e. GCF of 105,150,210 is 15 .

LCM of Denominators means LCM of 36,54,126 as per the given fractions.

LCM of 36,54,126 is 756 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 105,150,210

3 | 105, 150, 210 |

5 | 35, 50, 70 |

7, 10, 14 |

∴ So the GCF of the given numbers is 3 x 5 = 15

**Factors of 105**

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

**Factors of 150**

List of positive integer factors of 150 that divides 150 without a remainder.

1,2,3,5,6,10,15,25,30,50,75,150

**Factors of 210**

List of positive integer factors of 210 that divides 210 without a remainder.

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

**Greatest Common Factor**

We found the factors 105,150,210 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 105,150,210 ** is **15**.

Lets's calculate LCM of 36,54,126

2 | 36, 54, 126 |

3 | 18, 27, 63 |

3 | 6, 9, 21 |

2, 3, 7 |

∴ So the LCM of the given numbers is 2 x 3 x 3 x 2 x 3 x 7 = 756

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/756

Therefore, the GCF of Fractions 105/36,150/54,210/126 is 15/756

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 36,54,126 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,54,126) = 18

common factors(in case of two or more numbers have common factors) = 18

GCF(36,54,126) x common factors =18 x 18 = 324

LCM(36,54,126) = ( 36 × 54 × 126 ) / 324

LCM(36,54,126) = 244944 / 324

LCM(36,54,126) = 756

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 105/36, 150/54, 210/126?

Answer: GCF of Numerators as per given numbers 105/36, 150/54, 210/126 is

GCF of Numerators i.e. for 105,150,210 is 15

LCM of denominators i.e. for 36,54,126 is 756.

Thus, GCF of Fractions is 15/756.Finally, GCF of Fractions for 105/36, 150/54, 210/126 is 15/756.