Get help with finding GCF of fractions 10/36, 12/60, 20/84, 25/108 using GCF of Fractions Calculator to know the result 1/3780 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 10/36, 12/60, 20/84, 25/108 is **1/3780**.

GCF(10/36, 12/60, 20/84, 25/108) = 1/3780

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

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

Given fractions are 10/36,12/60,20/84,25/108

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 10,12,20,25

Greatest Common Factor of Numerators i.e. GCF of 10,12,20,25 is 1 .

LCM of Denominators means LCM of 36,60,84,108 as per the given fractions.

LCM of 36,60,84,108 is 3780 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 10,12,20,25

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

**Factors of 10**

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

**Factors of 12**

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

1,2,3,4,6,12

**Factors of 20**

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

**Factors of 25**

List of positive integer factors of 25 that divides 25 without a remainder.

1,5,25

**Greatest Common Factor**

We found the factors 10,12,20,25 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 10,12,20,25 ** is **1**.

Lets's calculate LCM of 36,60,84,108

2 | 36, 60, 84, 108 |

2 | 18, 30, 42, 54 |

3 | 9, 15, 21, 27 |

3 | 3, 5, 7, 9 |

1, 5, 7, 3 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 1 x 5 x 7 x 3 = 3780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3780

Therefore, the GCF of Fractions 10/36,12/60,20/84,25/108 is 1/3780

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 36,60,84,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(36,60,84,108) = 12

common factors(in case of two or more numbers have common factors) = 432

GCF(36,60,84,108) x common factors =12 x 432 = 5184

LCM(36,60,84,108) = ( 36 × 60 × 84 × 108 ) / 5184

LCM(36,60,84,108) = 19595520 / 5184

LCM(36,60,84,108) = 3780

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 10/36, 12/60, 20/84, 25/108?

Answer: GCF of Numerators as per given numbers 10/36, 12/60, 20/84, 25/108 is

GCF of Numerators i.e. for 10,12,20,25 is 1

LCM of denominators i.e. for 36,60,84,108 is 3780.

Thus, GCF of Fractions is 1/3780.Finally, GCF of Fractions for 10/36, 12/60, 20/84, 25/108 is 1/3780.