# What is the Greatest Common Factor of 108 and 114?

Greatest common factor (GCF) of 108 and 114 is **6**.

GCF(108,114) = 6

We will now calculate the prime factors of **108 and 114**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 108 and 114.

## How to find the GCF of 108 and 114?

We will first find the prime factorization of 108 and 114. After we will calculate the factors of 108 and 114 and find the biggest common factor number .

### Step-1: Prime Factorization of 108

Prime factors of 108 are 2, 3. Prime factorization of **108** in exponential form is:

108 = 2^{2} × 3^{3}

### Step-2: Prime Factorization of 114

Prime factors of 114 are 2, 3, 19. Prime factorization of **114** in exponential form is:

114 = 2^{1} × 3^{1} × 19^{1}

### Step-3: Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54

### Step-4: Factors of 114

List of positive integer factors of 114 that divides 108 without a remainder.

1, 2, 3, 6, 19, 38, 57

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 108 and 114. The biggest common factor number is the **GCF** number.

So the **greatest common factor 108 and 114** is **6**.

Also check out the Least Common Multiple of 108 and 114

#### Related Greatest Common Factors of 108

- GCF of 108 and 112
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- GCF of 108 and 115
- GCF of 108 and 116
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#### Related Greatest Common Factors of 114

- GCF of 114 and 118
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- GCF of 114 and 123
- GCF of 114 and 124
- GCF of 114 and 125
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- GCF of 114 and 127
- GCF of 114 and 128
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- GCF of 114 and 132
- GCF of 114 and 133
- GCF of 114 and 134