# What is the Greatest Common Factor of 102 and 109?

Greatest common factor (GCF) of 102 and 109 is **1**.

GCF(102,109) = 1

We will now calculate the prime factors of **102 and 109**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 102 and 109.

## How to find the GCF of 102 and 109?

We will first find the prime factorization of 102 and 109. After we will calculate the factors of 102 and 109 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 109

Prime factors of 109 are 109. Prime factorization of **109** in exponential form is:

109 = 109^{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 109

List of positive integer factors of 109 that divides 102 without a remainder.

1

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 102 and 109. The biggest common factor number is the **GCF** number.

So the **greatest common factor 102 and 109** is **1**.

Also check out the Least Common Multiple of 102 and 109

#### Related Greatest Common Factors of 102

- GCF of 102 and 106
- GCF of 102 and 107
- GCF of 102 and 108
- GCF of 102 and 109
- GCF of 102 and 110
- GCF of 102 and 111
- GCF of 102 and 112
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- GCF of 102 and 121
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#### Related Greatest Common Factors of 109

- GCF of 109 and 113
- GCF of 109 and 114
- GCF of 109 and 115
- GCF of 109 and 116
- GCF of 109 and 117
- GCF of 109 and 118
- GCF of 109 and 119
- GCF of 109 and 120
- GCF of 109 and 121
- GCF of 109 and 122
- GCF of 109 and 123
- GCF of 109 and 124
- GCF of 109 and 125
- GCF of 109 and 126
- GCF of 109 and 127
- GCF of 109 and 128
- GCF of 109 and 129