What is the Greatest Common Factor of 32209 and 32224?

Greatest common factor (GCF) of 32209 and 32224 is 1.

GCF(32209,32224) = 1

We will now calculate the prime factors of 32209 and 32224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32209 and 32224.

How to find the GCF of 32209 and 32224?

We will first find the prime factorization of 32209 and 32224. After we will calculate the factors of 32209 and 32224 and find the biggest common factor number .

Step-1: Prime Factorization of 32209

Prime factors of 32209 are 31, 1039. Prime factorization of 32209 in exponential form is:

32209 = 31¹ × 1039¹

Step-2: Prime Factorization of 32224

Prime factors of 32224 are 2, 19, 53. Prime factorization of 32224 in exponential form is:

32224 = 2⁵ × 19¹ × 53¹

Step-3: Factors of 32209

List of positive integer factors of 32209 that divides 32209 without a remainder.

1, 31, 1039

Step-4: Factors of 32224

List of positive integer factors of 32224 that divides 32209 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 53, 76, 106, 152, 212, 304, 424, 608, 848, 1007, 1696, 2014, 4028, 8056, 16112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32209 and 32224. The biggest common factor number is the GCF number.
So the greatest common factor 32209 and 32224 is 1.

Also check out the Least Common Multiple of 32209 and 32224