Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 84, 96 i.e. 12 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 84 and 96 is **12**.

GCF(84,96) = 12

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

- Greatest Common Factor of 84 and 96 by prime factorization method
- Greatest Common Factor of 84 and 96 by matching factors method

**Prime Factorization of 84**

2 | 84 |

2 | 42 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 84 are 2,3,7. Prime factorization of **84** in exponential form is:

84 = 2^{2}×3^{1}×7^{1}

**Prime Factorization of 96**

2 | 96 |

2 | 48 |

2 | 24 |

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 96 are 2,3. Prime factorization of **96** in exponential form is:

96 = 2^{5}×3^{1}

∴ So by taking common prime factors GCF of 84 and 96 is 12

**Factors of 84**

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

**Factors of 96**

List of positive integer factors of 96 that divides 96 without a remainder.

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

**Greatest Common Factor**

We found the factors and prime factorization of 84 and 96. The biggest common factor number is the **GCF** number.

So the **greatest common factor 84 and 96** is **12**.

Also check out the Least Common Multiple of 84 and 96

(i) The GCF of 84 and 96 is associative

GCF of 84 and 96 = GCF of 96 and 84

1. What is the GCF of 84 and 96?

Answer: GCF of 84 and 96 is 12.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

3. What are the Factors of 96?

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

4. How to Find the GCF of 84 and 96?

Answer:

Greatest Common Factor of 84 and 96 = 12

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 96

96 = 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 = 2 x 2 x 3 = 12

Step 4: Therefore, the greatest common factor of 84 and 96 is 12