What is the Greatest Common Factor of 30974 and 30984?

Greatest common factor (GCF) of 30974 and 30984 is 2.

GCF(30974,30984) = 2

We will now calculate the prime factors of 30974 and 30984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30974 and 30984.

How to find the GCF of 30974 and 30984?

We will first find the prime factorization of 30974 and 30984. After we will calculate the factors of 30974 and 30984 and find the biggest common factor number .

Step-1: Prime Factorization of 30974

Prime factors of 30974 are 2, 17, 911. Prime factorization of 30974 in exponential form is:

30974 = 2¹ × 17¹ × 911¹

Step-2: Prime Factorization of 30984

Prime factors of 30984 are 2, 3, 1291. Prime factorization of 30984 in exponential form is:

30984 = 2³ × 3¹ × 1291¹

Step-3: Factors of 30974

List of positive integer factors of 30974 that divides 30974 without a remainder.

1, 2, 17, 34, 911, 1822, 15487

Step-4: Factors of 30984

List of positive integer factors of 30984 that divides 30974 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1291, 2582, 3873, 5164, 7746, 10328, 15492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30974 and 30984. The biggest common factor number is the GCF number.
So the greatest common factor 30974 and 30984 is 2.

Also check out the Least Common Multiple of 30974 and 30984