# What is the Greatest Common Factor of 68 and 75?

Greatest common factor (GCF) of 68 and 75 is **1**.

GCF(68,75) = 1

We will now calculate the prime factors of **68 and 75**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 68 and 75.

## How to find the GCF of 68 and 75?

We will first find the prime factorization of 68 and 75. After we will calculate the factors of 68 and 75 and find the biggest common factor number .

### Step-1: Prime Factorization of 68

Prime factors of 68 are 2, 17. Prime factorization of **68** in exponential form is:

68 = 2^{2} × 17^{1}

### Step-2: Prime Factorization of 75

Prime factors of 75 are 3, 5. Prime factorization of **75** in exponential form is:

75 = 3^{1} × 5^{2}

### Step-3: Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1, 2, 4, 17, 34

### Step-4: Factors of 75

List of positive integer factors of 75 that divides 68 without a remainder.

1, 3, 5, 15, 25

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68 and 75. The biggest common factor number is the **GCF** number.

So the **greatest common factor 68 and 75** is **1**.

Also check out the Least Common Multiple of 68 and 75