Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 189, 190 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 189 and 190 is **1**.

GCF(189,190) = 1

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

- Greatest Common Factor of 189 and 190 by prime factorization method
- Greatest Common Factor of 189 and 190 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 190**

2 | 190 |

5 | 95 |

19 | 19 |

1 |

Prime factors of 190 are 2,5,19. Prime factorization of **190** in exponential form is:

190 = 2^{1}×5^{1}×19^{1}

∴ So by taking common prime factors GCF of 189 and 190 is 1

**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 190**

List of positive integer factors of 190 that divides 190 without a remainder.

1,2,5,10,19,38,95,190

**Greatest Common Factor**

We found the factors and prime factorization of 189 and 190. The biggest common factor number is the **GCF** number.

So the **greatest common factor 189 and 190** is **1**.

Also check out the Least Common Multiple of 189 and 190

(i) The GCF of 189 and 190 is associative

GCF of 189 and 190 = GCF of 190 and 189

1. What is the GCF of 189 and 190?

Answer: GCF of 189 and 190 is 1.

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 190?

Answer: Factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190. There are 8 integers that are factors of 190. The greatest factor of 190 is 190.

4. How to Find the GCF of 189 and 190?

Answer:

Greatest Common Factor of 189 and 190 = 1

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 190

190 = 2 x 5 x 19

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 189 and 190 is 1