What is the Greatest Common Factor of 3 and 30?

Greatest common factor (GCF) of 3 and 30 is 3.

GCF(3,30) = 3

We will now calculate the prime factors of 3 and 30, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3 and 30.

How to find the GCF of 3 and 30?

We will first find the prime factorization of 3 and 30. After we will calculate the factors of 3 and 30 and find the biggest common factor number .

Step-1: Prime Factorization of 3

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

3 = 3¹

Step-2: Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 2¹ × 3¹ × 5¹

Step-3: Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

Step-4: Factors of 30

List of positive integer factors of 30 that divides 3 without a remainder.

1, 2, 3, 5, 6, 10, 15

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 3 and 30 is 3.

Also check out the Least Common Multiple of 3 and 30