What is the Greatest Common Factor of 11214 and 11229?

Greatest common factor (GCF) of 11214 and 11229 is 3.

GCF(11214,11229) = 3

We will now calculate the prime factors of 11214 and 11229, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11214 and 11229.

How to find the GCF of 11214 and 11229?

We will first find the prime factorization of 11214 and 11229. After we will calculate the factors of 11214 and 11229 and find the biggest common factor number .

Step-1: Prime Factorization of 11214

Prime factors of 11214 are 2, 3, 7, 89. Prime factorization of 11214 in exponential form is:

11214 = 2¹ × 3² × 7¹ × 89¹

Step-2: 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-3: Factors of 11214

List of positive integer factors of 11214 that divides 11214 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 89, 126, 178, 267, 534, 623, 801, 1246, 1602, 1869, 3738, 5607

Step-4: Factors of 11229

List of positive integer factors of 11229 that divides 11214 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11214 and 11229. The biggest common factor number is the GCF number.
So the greatest common factor 11214 and 11229 is 3.

Also check out the Least Common Multiple of 11214 and 11229