What is the Greatest Common Factor of 11498 and 11514?

Greatest common factor (GCF) of 11498 and 11514 is 2.

GCF(11498,11514) = 2

We will now calculate the prime factors of 11498 and 11514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11498 and 11514.

How to find the GCF of 11498 and 11514?

We will first find the prime factorization of 11498 and 11514. After we will calculate the factors of 11498 and 11514 and find the biggest common factor number .

Step-1: Prime Factorization of 11498

Prime factors of 11498 are 2, 5749. Prime factorization of 11498 in exponential form is:

11498 = 2¹ × 5749¹

Step-2: Prime Factorization of 11514

Prime factors of 11514 are 2, 3, 19, 101. Prime factorization of 11514 in exponential form is:

11514 = 2¹ × 3¹ × 19¹ × 101¹

Step-3: Factors of 11498

List of positive integer factors of 11498 that divides 11498 without a remainder.

1, 2, 5749

Step-4: Factors of 11514

List of positive integer factors of 11514 that divides 11498 without a remainder.

1, 2, 3, 6, 19, 38, 57, 101, 114, 202, 303, 606, 1919, 3838, 5757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11498 and 11514. The biggest common factor number is the GCF number.
So the greatest common factor 11498 and 11514 is 2.

Also check out the Least Common Multiple of 11498 and 11514