# What is the Greatest Common Factor of 34 and 40?

Greatest common factor (GCF) of 34 and 40 is **2**.

GCF(34,40) = 2

We will now calculate the prime factors of **34 and 40**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 34 and 40.

## How to find the GCF of 34 and 40?

We will first find the prime factorization of 34 and 40. After we will calculate the factors of 34 and 40 and find the biggest common factor number .

### Step-1: Prime Factorization of 34

Prime factors of 34 are 2, 17. Prime factorization of **34** in exponential form is:

34 = 2^{1} × 17^{1}

### Step-2: Prime Factorization of 40

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

40 = 2^{3} × 5^{1}

### Step-3: Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1, 2, 17

### Step-4: Factors of 40

List of positive integer factors of 40 that divides 34 without a remainder.

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

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34 and 40. The biggest common factor number is the **GCF** number.

So the **greatest common factor 34 and 40** is **2**.

Also check out the Least Common Multiple of 34 and 40