Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 16, 21 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 16 and 21 is **1**.

GCF(16,21) = 1

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

- Greatest Common Factor of 16 and 21 by prime factorization method
- Greatest Common Factor of 16 and 21 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 21**

3 | 21 |

7 | 7 |

1 |

Prime factors of 21 are 3.Prime factorization of **21** in exponential form is:

21 = 3^{1}×7^{1}

∴ So by taking common prime factors GCF of 16 and 21 is 1

**Factors of 16**

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

1,2,4,8,16

**Factors of 21**

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

**Greatest Common Factor**

We found the factors and prime factorization of 16 and 21. The biggest common factor number is the **GCF** number.

So the **greatest common factor 16 and 21** is **1**.

Also check out the Least Common Multiple of 16 and 21

(i) The GCF of 16 and 21 is associative

GCF of 16 and 21 = GCF of 21 and 16

1. What is the GCF of 16 and 21?

Answer: GCF of 16 and 21 is 1.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the GCF of 16 and 21?

Answer:

Greatest Common Factor of 16 and 21 = 1

Step 1: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 21

21 = 3 x 7

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 16 and 21 is 1