# What is the Greatest Common Factor of 85 and 101?

Greatest common factor (GCF) of 85 and 101 is **1**.

GCF(85,101) = 1

We will now calculate the prime factors of **85 and 101**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 85 and 101.

## How to find the GCF of 85 and 101?

We will first find the prime factorization of 85 and 101. After we will calculate the factors of 85 and 101 and find the biggest common factor number .

### Step-1: Prime Factorization of 85

Prime factors of 85 are 5, 17. Prime factorization of **85** in exponential form is:

85 = 5^{1} × 17^{1}

### Step-2: Prime Factorization of 101

Prime factors of 101 are 101. Prime factorization of **101** in exponential form is:

101 = 101^{1}

### Step-3: Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1, 5, 17

### Step-4: Factors of 101

List of positive integer factors of 101 that divides 85 without a remainder.

1

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85 and 101. The biggest common factor number is the **GCF** number.

So the **greatest common factor 85 and 101** is **1**.

Also check out the Least Common Multiple of 85 and 101

#### Related Greatest Common Factors of 85

#### Related Greatest Common Factors of 101

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