# What is the Greatest Common Factor of 44 and 51?

Greatest common factor (GCF) of 44 and 51 is **1**.

GCF(44,51) = 1

We will now calculate the prime factors of **44 and 51**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 44 and 51.

## How to find the GCF of 44 and 51?

We will first find the prime factorization of 44 and 51. After we will calculate the factors of 44 and 51 and find the biggest common factor number .

### Step-1: Prime Factorization of 44

Prime factors of 44 are 2, 11. Prime factorization of **44** in exponential form is:

44 = 2^{2} × 11^{1}

### Step-2: Prime Factorization of 51

Prime factors of 51 are 3, 17. Prime factorization of **51** in exponential form is:

51 = 3^{1} × 17^{1}

### Step-3: Factors of 44

List of positive integer factors of 44 that divides 44 without a remainder.

1, 2, 4, 11, 22

### Step-4: Factors of 51

List of positive integer factors of 51 that divides 44 without a remainder.

1, 3, 17

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 44 and 51. The biggest common factor number is the **GCF** number.

So the **greatest common factor 44 and 51** is **1**.

Also check out the Least Common Multiple of 44 and 51