What is the Greatest Common Factor of 53209 and 53222?

Greatest common factor (GCF) of 53209 and 53222 is 13.

GCF(53209,53222) = 13

We will now calculate the prime factors of 53209 and 53222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53209 and 53222.

How to find the GCF of 53209 and 53222?

We will first find the prime factorization of 53209 and 53222. After we will calculate the factors of 53209 and 53222 and find the biggest common factor number .

Step-1: Prime Factorization of 53209

Prime factors of 53209 are 13, 4093. Prime factorization of 53209 in exponential form is:

53209 = 13¹ × 4093¹

Step-2: Prime Factorization of 53222

Prime factors of 53222 are 2, 13, 23, 89. Prime factorization of 53222 in exponential form is:

53222 = 2¹ × 13¹ × 23¹ × 89¹

Step-3: Factors of 53209

List of positive integer factors of 53209 that divides 53209 without a remainder.

1, 13, 4093

Step-4: Factors of 53222

List of positive integer factors of 53222 that divides 53209 without a remainder.

1, 2, 13, 23, 26, 46, 89, 178, 299, 598, 1157, 2047, 2314, 4094, 26611

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53209 and 53222. The biggest common factor number is the GCF number.
So the greatest common factor 53209 and 53222 is 13.

Also check out the Least Common Multiple of 53209 and 53222