# What is the Greatest Common Factor of 75 and 84?

Greatest common factor (GCF) of 75 and 84 is 3.

GCF(75,84) = 3

We will now calculate the prime factors of 75 and 84, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75 and 84.

GCF Calculator and
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## How to find the GCF of 75 and 84?

We will first find the prime factorization of 75 and 84. After we will calculate the factors of 75 and 84 and find the biggest common factor number .

### Step-1: Prime Factorization of 75

Prime factors of 75 are 3, 5. Prime factorization of 75 in exponential form is:

75 = 31 × 52

### Step-2: Prime Factorization of 84

Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:

84 = 22 × 31 × 71

### Step-3: Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1, 3, 5, 15, 25

### Step-4: Factors of 84

List of positive integer factors of 84 that divides 75 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75 and 84. The biggest common factor number is the GCF number.
So the greatest common factor 75 and 84 is 3.

Also check out the Least Common Multiple of 75 and 84