What is the Greatest Common Factor of 30 and 46?

Greatest common factor (GCF) of 30 and 46 is 2.

GCF(30,46) = 2

We will now calculate the prime factors of 30 and 46, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 46.

How to find the GCF of 30 and 46?

We will first find the prime factorization of 30 and 46. After we will calculate the factors of 30 and 46 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 46

Prime factors of 46 are 2, 23. Prime factorization of 46 in exponential form is:

46 = 2¹ × 23¹

Step-3: Factors of 30

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

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

Step-4: Factors of 46

List of positive integer factors of 46 that divides 30 without a remainder.

1, 2, 23

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 46. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 46 is 2.

Also check out the Least Common Multiple of 30 and 46