What is the Greatest Common Factor of 14578 and 14596?

Greatest common factor (GCF) of 14578 and 14596 is 2.

GCF(14578,14596) = 2

We will now calculate the prime factors of 14578 and 14596, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14578 and 14596.

How to find the GCF of 14578 and 14596?

We will first find the prime factorization of 14578 and 14596. After we will calculate the factors of 14578 and 14596 and find the biggest common factor number .

Step-1: Prime Factorization of 14578

Prime factors of 14578 are 2, 37, 197. Prime factorization of 14578 in exponential form is:

14578 = 2¹ × 37¹ × 197¹

Step-2: Prime Factorization of 14596

Prime factors of 14596 are 2, 41, 89. Prime factorization of 14596 in exponential form is:

14596 = 2² × 41¹ × 89¹

Step-3: Factors of 14578

List of positive integer factors of 14578 that divides 14578 without a remainder.

1, 2, 37, 74, 197, 394, 7289

Step-4: Factors of 14596

List of positive integer factors of 14596 that divides 14578 without a remainder.

1, 2, 4, 41, 82, 89, 164, 178, 356, 3649, 7298

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14578 and 14596. The biggest common factor number is the GCF number.
So the greatest common factor 14578 and 14596 is 2.

Also check out the Least Common Multiple of 14578 and 14596