Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1800, 1803 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1800 and 1803 is **3**.

GCF(1800,1803) = 3

*Greatest common factor* or Greatest common divisor (GCD) can be calculated in following way;

- Greatest Common Factor of 1800 and 1803 by prime factorization method
- Greatest Common Factor of 1800 and 1803 by matching factors method

**Prime Factorization of 1800**

2 | 1800 |

2 | 900 |

2 | 450 |

3 | 225 |

3 | 75 |

5 | 25 |

5 | 5 |

1 |

Prime factors of 1800 are 2,3,5. Prime factorization of **1800** in exponential form is:

1800 = 2^{3}×3^{2}×5^{2}

**Prime Factorization of 1803**

3 | 1803 |

601 | 601 |

1 |

Prime factors of 1803 are 3,601. Prime factorization of **1803** in exponential form is:

1803 = 3^{1}×601^{1}

∴ So by taking common prime factors GCF of 1800 and 1803 is 3

**Factors of 1800**

List of positive integer factors of 1800 that divides 1800 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,18,20,24,25,30,36,40,45,50,60,72,75,90,100,120,150,180,200,225,300,360,450,600,900,1800

**Factors of 1803**

List of positive integer factors of 1803 that divides 1803 without a remainder.

1,3,601,1803

**Greatest Common Factor**

We found the factors and prime factorization of 1800 and 1803. The biggest common factor number is the **GCF** number.

So the **greatest common factor 1800 and 1803** is **3**.

Also check out the Least Common Multiple of 1800 and 1803

(i) The GCF of 1800 and 1803 is associative

GCF of 1800 and 1803 = GCF of 1803 and 1800

1. What is the GCF of 1800 and 1803?

Answer: GCF of 1800 and 1803 is 3.

2. What are the Factors of 1800?

Answer: Factors of 1800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800. There are 36 integers that are factors of 1800. The greatest factor of 1800 is 1800.

3. What are the Factors of 1803?

Answer: Factors of 1803 are 1, 3, 601, 1803. There are 4 integers that are factors of 1803. The greatest factor of 1803 is 1803.

4. How to Find the GCF of 1800 and 1803?

Answer:

Greatest Common Factor of 1800 and 1803 = 3

Step 1: Find the prime factorization of 1800

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 1803

1803 = 3 x 601

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 1800 and 1803 is 3