# What is the Greatest Common Factor of 105 and 120?

Greatest common factor (GCF) of 105 and 120 is **15**.

GCF(105,120) = 15

We will now calculate the prime factors of **105 and 120**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 105 and 120.

## How to find the GCF of 105 and 120?

We will first find the prime factorization of 105 and 120. After we will calculate the factors of 105 and 120 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 = 3^{1} × 5^{1} × 7^{1}

### Step-2: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of **120** in exponential form is:

120 = 2^{3} × 3^{1} × 5^{1}

### 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 120

List of positive integer factors of 120 that divides 105 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 120. The biggest common factor number is the **GCF** number.

So the **greatest common factor 105 and 120** is **15**.

Also check out the Least Common Multiple of 105 and 120

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#### Related Greatest Common Factors of 120

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