Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 189, 192 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 189 and 192 is **3**.

GCF(189,192) = 3

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

- Greatest Common Factor of 189 and 192 by prime factorization method
- Greatest Common Factor of 189 and 192 by matching factors method

**Prime Factorization of 189**

3 | 189 |

3 | 63 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 189 are 3,7. Prime factorization of **189** in exponential form is:

189 = 3^{3}×7^{1}

**Prime Factorization of 192**

2 | 192 |

2 | 96 |

2 | 48 |

2 | 24 |

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 192 are 2,3. Prime factorization of **192** in exponential form is:

192 = 2^{6}×3^{1}

∴ So by taking common prime factors GCF of 189 and 192 is 3

**Factors of 189**

List of positive integer factors of 189 that divides 189 without a remainder.

1,3,7,9,21,27,63,189

**Factors of 192**

List of positive integer factors of 192 that divides 192 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,64,96,192

**Greatest Common Factor**

We found the factors and prime factorization of 189 and 192. The biggest common factor number is the **GCF** number.

So the **greatest common factor 189 and 192** is **3**.

Also check out the Least Common Multiple of 189 and 192

(i) The GCF of 189 and 192 is associative

GCF of 189 and 192 = GCF of 192 and 189

1. What is the GCF of 189 and 192?

Answer: GCF of 189 and 192 is 3.

2. What are the Factors of 189?

Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.

3. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

4. How to Find the GCF of 189 and 192?

Answer:

Greatest Common Factor of 189 and 192 = 3

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

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 189 and 192 is 3