Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 28, 32 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 28 and 32 is **4**.

GCF(28,32) = 4

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

- Greatest Common Factor of 28 and 32 by prime factorization method
- Greatest Common Factor of 28 and 32 by matching factors method

**Prime Factorization of 28**

2 | 28 |

2 | 14 |

7 | 7 |

1 |

Prime factors of 28 are 2,7. Prime factorization of **28** in exponential form is:

28 = 2^{2}×7^{1}

**Prime Factorization of 32**

2 | 32 |

2 | 16 |

2 | 8 |

2 | 4 |

2 | 2 |

1 |

Prime factors of 32 are 2. Prime factorization of **32** in exponential form is:

32 = 2^{5}

∴ So by taking common prime factors GCF of 28 and 32 is 4

**Factors of 28**

List of positive integer factors of 28 that divides 28 without a remainder.

1,2,4,7,14,28

**Factors of 32**

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

**Greatest Common Factor**

We found the factors and prime factorization of 28 and 32. The biggest common factor number is the **GCF** number.

So the **greatest common factor 28 and 32** is **4**.

Also check out the Least Common Multiple of 28 and 32

(i) The GCF of 28 and 32 is associative

GCF of 28 and 32 = GCF of 32 and 28

1. What is the GCF of 28 and 32?

Answer: GCF of 28 and 32 is 4.

2. What are the Factors of 28?

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

3. What are the Factors of 32?

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

4. How to Find the GCF of 28 and 32?

Answer:

Greatest Common Factor of 28 and 32 = 4

Step 1: Find the prime factorization of 28

28 = 2 x 2 x 7

Step 2: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

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 28 and 32 is 4