What is the Greatest Common Factor of 11229 and 11248?

Greatest common factor (GCF) of 11229 and 11248 is 19.

GCF(11229,11248) = 19

We will now calculate the prime factors of 11229 and 11248, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11229 and 11248.

How to find the GCF of 11229 and 11248?

We will first find the prime factorization of 11229 and 11248. After we will calculate the factors of 11229 and 11248 and find the biggest common factor number .

Step-1: Prime Factorization of 11229

Prime factors of 11229 are 3, 19, 197. Prime factorization of 11229 in exponential form is:

11229 = 3¹ × 19¹ × 197¹

Step-2: Prime Factorization of 11248

Prime factors of 11248 are 2, 19, 37. Prime factorization of 11248 in exponential form is:

11248 = 2⁴ × 19¹ × 37¹

Step-3: Factors of 11229

List of positive integer factors of 11229 that divides 11229 without a remainder.

1, 3, 19, 57, 197, 591, 3743

Step-4: Factors of 11248

List of positive integer factors of 11248 that divides 11229 without a remainder.

1, 2, 4, 8, 16, 19, 37, 38, 74, 76, 148, 152, 296, 304, 592, 703, 1406, 2812, 5624

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11229 and 11248. The biggest common factor number is the GCF number.
So the greatest common factor 11229 and 11248 is 19.

Also check out the Least Common Multiple of 11229 and 11248