What is the Greatest Common Factor of 22274 and 22288?

Greatest common factor (GCF) of 22274 and 22288 is 14.

GCF(22274,22288) = 14

We will now calculate the prime factors of 22274 and 22288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22274 and 22288.

How to find the GCF of 22274 and 22288?

We will first find the prime factorization of 22274 and 22288. After we will calculate the factors of 22274 and 22288 and find the biggest common factor number .

Step-1: Prime Factorization of 22274

Prime factors of 22274 are 2, 7, 37, 43. Prime factorization of 22274 in exponential form is:

22274 = 2¹ × 7¹ × 37¹ × 43¹

Step-2: Prime Factorization of 22288

Prime factors of 22288 are 2, 7, 199. Prime factorization of 22288 in exponential form is:

22288 = 2⁴ × 7¹ × 199¹

Step-3: Factors of 22274

List of positive integer factors of 22274 that divides 22274 without a remainder.

1, 2, 7, 14, 37, 43, 74, 86, 259, 301, 518, 602, 1591, 3182, 11137

Step-4: Factors of 22288

List of positive integer factors of 22288 that divides 22274 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 199, 398, 796, 1393, 1592, 2786, 3184, 5572, 11144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22274 and 22288. The biggest common factor number is the GCF number.
So the greatest common factor 22274 and 22288 is 14.

Also check out the Least Common Multiple of 22274 and 22288