Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 16, 36 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 16 and 36 is **4**.

GCF(16,36) = 4

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

- Greatest Common Factor of 16 and 36 by prime factorization method
- Greatest Common Factor of 16 and 36 by matching factors method

**Prime Factorization of 16**

2 | 16 |

2 | 8 |

2 | 4 |

2 | 2 |

1 |

Prime factors of 16 are 2. Prime factorization of **16** in exponential form is:

16 = 2^{4}

**Prime Factorization of 36**

2 | 36 |

2 | 18 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 36 are 2.Prime factorization of **36** in exponential form is:

36 = 2^{2}×3^{2}

∴ So by taking common prime factors GCF of 16 and 36 is 4

**Factors of 16**

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

**Factors of 36**

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

**Greatest Common Factor**

We found the factors and prime factorization of 16 and 36. The biggest common factor number is the **GCF** number.

So the **greatest common factor 16 and 36** is **4**.

Also check out the Least Common Multiple of 16 and 36

(i) The GCF of 16 and 36 is associative

GCF of 16 and 36 = GCF of 36 and 16

1. What is the GCF of 16 and 36?

Answer: GCF of 16 and 36 is 4.

2. What are the Factors of 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

3. What are the Factors of 36?

Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.

4. How to Find the GCF of 16 and 36?

Answer:

Greatest Common Factor of 16 and 36 = 4

Step 1: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 16 and 36 is 4