What is the Greatest Common Factor of 33969 and 33982?

Greatest common factor (GCF) of 33969 and 33982 is 13.

GCF(33969,33982) = 13

We will now calculate the prime factors of 33969 and 33982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33969 and 33982.

How to find the GCF of 33969 and 33982?

We will first find the prime factorization of 33969 and 33982. After we will calculate the factors of 33969 and 33982 and find the biggest common factor number .

Step-1: Prime Factorization of 33969

Prime factors of 33969 are 3, 13, 67. Prime factorization of 33969 in exponential form is:

33969 = 3¹ × 13² × 67¹

Step-2: Prime Factorization of 33982

Prime factors of 33982 are 2, 13, 1307. Prime factorization of 33982 in exponential form is:

33982 = 2¹ × 13¹ × 1307¹

Step-3: Factors of 33969

List of positive integer factors of 33969 that divides 33969 without a remainder.

1, 3, 13, 39, 67, 169, 201, 507, 871, 2613, 11323

Step-4: Factors of 33982

List of positive integer factors of 33982 that divides 33969 without a remainder.

1, 2, 13, 26, 1307, 2614, 16991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33969 and 33982. The biggest common factor number is the GCF number.
So the greatest common factor 33969 and 33982 is 13.

Also check out the Least Common Multiple of 33969 and 33982