Get help with finding GCF of fractions 1000/288, 1440/864 using GCF of Fractions Calculator to know the result 40/864 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 1000/288, 1440/864 is **40/864**.

GCF(1000/288, 1440/864) = 40/864

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

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

Given fractions are 1000/288,1440/864

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 1000,1440

Greatest Common Factor of Numerators i.e. GCF of 1000,1440 is 40 .

LCM of Denominators means LCM of 288,864 as per the given fractions.

LCM of 288,864 is 864 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 1000,1440

2 | 1000, 1440 |

2 | 500, 720 |

2 | 250, 360 |

5 | 125, 180 |

25, 36 |

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

**Factors of 1000**

List of positive integer factors of 1000 that divides 1000 without a remainder.

1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000

**Factors of 1440**

List of positive integer factors of 1440 that divides 1440 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,32,36,40,45,48,60,72,80,90,96,120,144,160,180,240,288,360,480,720,1440

**Greatest Common Factor**

We found the factors 1000,1440 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 1000,1440 ** is **40**.

Lets's calculate LCM of 288,864

2 | 288, 864 |

2 | 144, 432 |

2 | 72, 216 |

2 | 36, 108 |

2 | 18, 54 |

3 | 9, 27 |

3 | 3, 9 |

1, 3 |

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 1 x 3 = 864

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/864

Therefore, the GCF of Fractions 1000/288,1440/864 is 40/864

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 288,864 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(288,864) = 288

common factors(in case of two or more numbers have common factors) = 1

GCF(288,864) x common factors =288 x 1 = 288

LCM(288,864) = ( 288 × 864 ) / 288

LCM(288,864) = 248832 / 288

LCM(288,864) = 864

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 1000/288, 1440/864?

Answer: GCF of Numerators as per given numbers 1000/288, 1440/864 is

GCF of Numerators i.e. for 1000,1440 is 40

LCM of denominators i.e. for 288,864 is 864.

Thus, GCF of Fractions is 40/864.Finally, GCF of Fractions for 1000/288, 1440/864 is 40/864.