# What is the Greatest Common Factor of 105 and 116?

Greatest common factor (GCF) of 105 and 116 is 1.

GCF(105,116) = 1

We will now calculate the prime factors of 105 and 116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 116.

GCF Calculator and
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## How to find the GCF of 105 and 116?

We will first find the prime factorization of 105 and 116. After we will calculate the factors of 105 and 116 and find the biggest common factor number .

### Step-1: Prime Factorization of 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 31 × 51 × 71

### Step-2: Prime Factorization of 116

Prime factors of 116 are 2, 29. Prime factorization of 116 in exponential form is:

116 = 22 × 291

### Step-3: Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35

### Step-4: Factors of 116

List of positive integer factors of 116 that divides 105 without a remainder.

1, 2, 4, 29, 58

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 116. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 116 is 1.

Also check out the Least Common Multiple of 105 and 116