# What is the Greatest Common Factor of 102 and 117?

Greatest common factor (GCF) of 102 and 117 is **3**.

GCF(102,117) = 3

We will now calculate the prime factors of **102 and 117**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 102 and 117.

## How to find the GCF of 102 and 117?

We will first find the prime factorization of 102 and 117. After we will calculate the factors of 102 and 117 and find the biggest common factor number .

### Step-1: Prime Factorization of 102

Prime factors of 102 are 2, 3, 17. Prime factorization of **102** in exponential form is:

102 = 2^{1} × 3^{1} × 17^{1}

### Step-2: Prime Factorization of 117

Prime factors of 117 are 3, 13. Prime factorization of **117** in exponential form is:

117 = 3^{2} × 13^{1}

### Step-3: Factors of 102

List of positive integer factors of 102 that divides 102 without a remainder.

1, 2, 3, 6, 17, 34, 51

### Step-4: Factors of 117

List of positive integer factors of 117 that divides 102 without a remainder.

1, 3, 9, 13, 39

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 102 and 117. The biggest common factor number is the **GCF** number.

So the **greatest common factor 102 and 117** is **3**.

Also check out the Least Common Multiple of 102 and 117

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#### Related Greatest Common Factors of 117

- GCF of 117 and 121
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