Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 40, 52 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 40 and 52 is **4**.

GCF(40,52) = 4

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

- Greatest Common Factor of 40 and 52 by prime factorization method
- Greatest Common Factor of 40 and 52 by matching factors method

**Prime Factorization of 40**

2 | 40 |

2 | 20 |

2 | 10 |

5 | 5 |

1 |

Prime factors of 40 are 2,5. Prime factorization of **40** in exponential form is:

40 = 2^{3}×5^{1}

**Prime Factorization of 52**

2 | 52 |

2 | 26 |

13 | 13 |

1 |

Prime factors of 52 are 2,13. Prime factorization of **52** in exponential form is:

52 = 2^{2}×13^{1}

∴ So by taking common prime factors GCF of 40 and 52 is 4

**Factors of 40**

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

**Factors of 52**

List of positive integer factors of 52 that divides 52 without a remainder.

1,2,4,13,26,52

**Greatest Common Factor**

We found the factors and prime factorization of 40 and 52. The biggest common factor number is the **GCF** number.

So the **greatest common factor 40 and 52** is **4**.

Also check out the Least Common Multiple of 40 and 52

(i) The GCF of 40 and 52 is associative

GCF of 40 and 52 = GCF of 52 and 40

1. What is the GCF of 40 and 52?

Answer: GCF of 40 and 52 is 4.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

3. What are the Factors of 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

4. How to Find the GCF of 40 and 52?

Answer:

Greatest Common Factor of 40 and 52 = 4

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 52

52 = 2 x 2 x 13

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 40 and 52 is 4