What is the Greatest Common Factor of 32204 and 32208?

Greatest common factor (GCF) of 32204 and 32208 is 4.

GCF(32204,32208) = 4

We will now calculate the prime factors of 32204 and 32208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32204 and 32208.

How to find the GCF of 32204 and 32208?

We will first find the prime factorization of 32204 and 32208. After we will calculate the factors of 32204 and 32208 and find the biggest common factor number .

Step-1: Prime Factorization of 32204

Prime factors of 32204 are 2, 83, 97. Prime factorization of 32204 in exponential form is:

32204 = 2² × 83¹ × 97¹

Step-2: Prime Factorization of 32208

Prime factors of 32208 are 2, 3, 11, 61. Prime factorization of 32208 in exponential form is:

32208 = 2⁴ × 3¹ × 11¹ × 61¹

Step-3: Factors of 32204

List of positive integer factors of 32204 that divides 32204 without a remainder.

1, 2, 4, 83, 97, 166, 194, 332, 388, 8051, 16102

Step-4: Factors of 32208

List of positive integer factors of 32208 that divides 32204 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 61, 66, 88, 122, 132, 176, 183, 244, 264, 366, 488, 528, 671, 732, 976, 1342, 1464, 2013, 2684, 2928, 4026, 5368, 8052, 10736, 16104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32204 and 32208. The biggest common factor number is the GCF number.
So the greatest common factor 32204 and 32208 is 4.

Also check out the Least Common Multiple of 32204 and 32208