# What is the Greatest Common Factor of 45 and 59?

Greatest common factor (GCF) of 45 and 59 is **1**.

GCF(45,59) = 1

We will now calculate the prime factors of **45 and 59**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 45 and 59.

## How to find the GCF of 45 and 59?

We will first find the prime factorization of 45 and 59. After we will calculate the factors of 45 and 59 and find the biggest common factor number .

### Step-1: Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of **45** in exponential form is:

45 = 3^{2} × 5^{1}

### Step-2: Prime Factorization of 59

Prime factors of 59 are 59. Prime factorization of **59** in exponential form is:

59 = 59^{1}

### Step-3: Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15

### Step-4: Factors of 59

List of positive integer factors of 59 that divides 45 without a remainder.

1

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45 and 59. The biggest common factor number is the **GCF** number.

So the **greatest common factor 45 and 59** is **1**.

Also check out the Least Common Multiple of 45 and 59