Get help with finding GCF of fractions 65/75, 30/40, 50/60 using GCF of Fractions Calculator to know the result 5/600 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 65/75, 30/40, 50/60 is **5/600**.

GCF(65/75, 30/40, 50/60) = 5/600

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

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

Given fractions are 65/75,30/40,50/60

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 65,30,50

Greatest Common Factor of Numerators i.e. GCF of 65,30,50 is 5 .

LCM of Denominators means LCM of 75,40,60 as per the given fractions.

LCM of 75,40,60 is 600 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 65,30,50

5 | 65, 30, 50 |

13, 6, 10 |

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

**Factors of 65**

List of positive integer factors of 65 that divides 65 without a remainder.

1,5,13,65

**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 50**

List of positive integer factors of 50 that divides 50 without a remainder.

1,2,5,10,25,50

**Greatest Common Factor**

We found the factors 65,30,50 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 65,30,50 ** is **5**.

Lets's calculate LCM of 75,40,60

2 | 75, 40, 60 |

2 | 75, 20, 30 |

3 | 75, 10, 15 |

5 | 25, 10, 5 |

1, 2, 5 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 2 x 5 = 600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/600

Therefore, the GCF of Fractions 65/75,30/40,50/60 is 5/600

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 75,40,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,40,60) = 5

common factors(in case of two or more numbers have common factors) = 60

GCF(75,40,60) x common factors =5 x 60 = 300

LCM(75,40,60) = ( 75 × 40 × 60 ) / 300

LCM(75,40,60) = 180000 / 300

LCM(75,40,60) = 600

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 65/75, 30/40, 50/60?

Answer: GCF of Numerators as per given numbers 65/75, 30/40, 50/60 is

GCF of Numerators i.e. for 65,30,50 is 5

LCM of denominators i.e. for 75,40,60 is 600.

Thus, GCF of Fractions is 5/600.Finally, GCF of Fractions for 65/75, 30/40, 50/60 is 5/600.