What is the Greatest Common Factor of 33664 and 33670?

Greatest common factor (GCF) of 33664 and 33670 is 2.

GCF(33664,33670) = 2

We will now calculate the prime factors of 33664 and 33670, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33664 and 33670.

How to find the GCF of 33664 and 33670?

We will first find the prime factorization of 33664 and 33670. After we will calculate the factors of 33664 and 33670 and find the biggest common factor number .

Step-1: Prime Factorization of 33664

Prime factors of 33664 are 2, 263. Prime factorization of 33664 in exponential form is:

33664 = 2⁷ × 263¹

Step-2: Prime Factorization of 33670

Prime factors of 33670 are 2, 5, 7, 13, 37. Prime factorization of 33670 in exponential form is:

33670 = 2¹ × 5¹ × 7¹ × 13¹ × 37¹

Step-3: Factors of 33664

List of positive integer factors of 33664 that divides 33664 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 263, 526, 1052, 2104, 4208, 8416, 16832

Step-4: Factors of 33670

List of positive integer factors of 33670 that divides 33664 without a remainder.

1, 2, 5, 7, 10, 13, 14, 26, 35, 37, 65, 70, 74, 91, 130, 182, 185, 259, 370, 455, 481, 518, 910, 962, 1295, 2405, 2590, 3367, 4810, 6734, 16835

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33664 and 33670. The biggest common factor number is the GCF number.
So the greatest common factor 33664 and 33670 is 2.

Also check out the Least Common Multiple of 33664 and 33670