What is the Greatest Common Factor of 82214 and 82225?

Greatest common factor (GCF) of 82214 and 82225 is 11.

GCF(82214,82225) = 11

We will now calculate the prime factors of 82214 and 82225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82214 and 82225.

How to find the GCF of 82214 and 82225?

We will first find the prime factorization of 82214 and 82225. After we will calculate the factors of 82214 and 82225 and find the biggest common factor number .

Step-1: Prime Factorization of 82214

Prime factors of 82214 are 2, 11, 37, 101. Prime factorization of 82214 in exponential form is:

82214 = 2¹ × 11¹ × 37¹ × 101¹

Step-2: Prime Factorization of 82225

Prime factors of 82225 are 5, 11, 13, 23. Prime factorization of 82225 in exponential form is:

82225 = 5² × 11¹ × 13¹ × 23¹

Step-3: Factors of 82214

List of positive integer factors of 82214 that divides 82214 without a remainder.

1, 2, 11, 22, 37, 74, 101, 202, 407, 814, 1111, 2222, 3737, 7474, 41107

Step-4: Factors of 82225

List of positive integer factors of 82225 that divides 82214 without a remainder.

1, 5, 11, 13, 23, 25, 55, 65, 115, 143, 253, 275, 299, 325, 575, 715, 1265, 1495, 3289, 3575, 6325, 7475, 16445

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82214 and 82225. The biggest common factor number is the GCF number.
So the greatest common factor 82214 and 82225 is 11.

Also check out the Least Common Multiple of 82214 and 82225