What is the Greatest Common Factor of 17000 and 17004?

Greatest common factor (GCF) of 17000 and 17004 is 4.

GCF(17000,17004) = 4

We will now calculate the prime factors of 17000 and 17004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17000 and 17004.

How to find the GCF of 17000 and 17004?

We will first find the prime factorization of 17000 and 17004. After we will calculate the factors of 17000 and 17004 and find the biggest common factor number .

Step-1: Prime Factorization of 17000

Prime factors of 17000 are 2, 5, 17. Prime factorization of 17000 in exponential form is:

17000 = 2³ × 5³ × 17¹

Step-2: Prime Factorization of 17004

Prime factors of 17004 are 2, 3, 13, 109. Prime factorization of 17004 in exponential form is:

17004 = 2² × 3¹ × 13¹ × 109¹

Step-3: Factors of 17000

List of positive integer factors of 17000 that divides 17000 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 125, 136, 170, 200, 250, 340, 425, 500, 680, 850, 1000, 1700, 2125, 3400, 4250, 8500

Step-4: Factors of 17004

List of positive integer factors of 17004 that divides 17000 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 109, 156, 218, 327, 436, 654, 1308, 1417, 2834, 4251, 5668, 8502

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17000 and 17004. The biggest common factor number is the GCF number.
So the greatest common factor 17000 and 17004 is 4.

Also check out the Least Common Multiple of 17000 and 17004