# What is the Greatest Common Factor of 71 and 84?

Greatest common factor (GCF) of 71 and 84 is **1**.

GCF(71,84) = 1

We will now calculate the prime factors of **71 and 84**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 71 and 84.

## How to find the GCF of 71 and 84?

We will first find the prime factorization of 71 and 84. After we will calculate the factors of 71 and 84 and find the biggest common factor number .

### Step-1: Prime Factorization of 71

Prime factors of 71 are 71. Prime factorization of **71** in exponential form is:

71 = 71^{1}

### Step-2: Prime Factorization of 84

Prime factors of 84 are 2, 3, 7. Prime factorization of **84** in exponential form is:

84 = 2^{2} × 3^{1} × 7^{1}

### Step-3: Factors of 71

List of positive integer factors of 71 that divides 71 without a remainder.

1

### Step-4: Factors of 84

List of positive integer factors of 84 that divides 71 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71 and 84. The biggest common factor number is the **GCF** number.

So the **greatest common factor 71 and 84** is **1**.

Also check out the Least Common Multiple of 71 and 84