Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 16, 22 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 16 and 22 is **2**.

GCF(16,22) = 2

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

- Greatest Common Factor of 16 and 22 by prime factorization method
- Greatest Common Factor of 16 and 22 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 22**

2 | 22 |

11 | 11 |

1 |

Prime factors of 22 are 2.Prime factorization of **22** in exponential form is:

22 = 2^{1}×11^{1}

∴ So by taking common prime factors GCF of 16 and 22 is 2

**Factors of 16**

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

1,2,4,8,16

**Factors of 22**

List of positive integer factors of 22 that divides 22 without a remainder.

1,2,11,22

**Greatest Common Factor**

We found the factors and prime factorization of 16 and 22. The biggest common factor number is the **GCF** number.

So the **greatest common factor 16 and 22** is **2**.

Also check out the Least Common Multiple of 16 and 22

(i) The GCF of 16 and 22 is associative

GCF of 16 and 22 = GCF of 22 and 16

1. What is the GCF of 16 and 22?

Answer: GCF of 16 and 22 is 2.

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 22?

Answer: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22.

4. How to Find the GCF of 16 and 22?

Answer:

Greatest Common Factor of 16 and 22 = 2

Step 1: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 22

22 = 2 x 11

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

GCF = 2

Step 4: Therefore, the greatest common factor of 16 and 22 is 2