What is the Greatest Common Factor of 20498 and 20514?

Greatest common factor (GCF) of 20498 and 20514 is 2.

GCF(20498,20514) = 2

We will now calculate the prime factors of 20498 and 20514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20498 and 20514.

How to find the GCF of 20498 and 20514?

We will first find the prime factorization of 20498 and 20514. After we will calculate the factors of 20498 and 20514 and find the biggest common factor number .

Step-1: Prime Factorization of 20498

Prime factors of 20498 are 2, 37, 277. Prime factorization of 20498 in exponential form is:

20498 = 2¹ × 37¹ × 277¹

Step-2: Prime Factorization of 20514

Prime factors of 20514 are 2, 3, 13, 263. Prime factorization of 20514 in exponential form is:

20514 = 2¹ × 3¹ × 13¹ × 263¹

Step-3: Factors of 20498

List of positive integer factors of 20498 that divides 20498 without a remainder.

1, 2, 37, 74, 277, 554, 10249

Step-4: Factors of 20514

List of positive integer factors of 20514 that divides 20498 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 263, 526, 789, 1578, 3419, 6838, 10257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20498 and 20514. The biggest common factor number is the GCF number.
So the greatest common factor 20498 and 20514 is 2.

Also check out the Least Common Multiple of 20498 and 20514