What is the Greatest Common Factor of 66000 and 66004?

Greatest common factor (GCF) of 66000 and 66004 is 4.

GCF(66000,66004) = 4

We will now calculate the prime factors of 66000 and 66004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66000 and 66004.

How to find the GCF of 66000 and 66004?

We will first find the prime factorization of 66000 and 66004. After we will calculate the factors of 66000 and 66004 and find the biggest common factor number .

Step-1: Prime Factorization of 66000

Prime factors of 66000 are 2, 3, 5, 11. Prime factorization of 66000 in exponential form is:

66000 = 2⁴ × 3¹ × 5³ × 11¹

Step-2: Prime Factorization of 66004

Prime factors of 66004 are 2, 29, 569. Prime factorization of 66004 in exponential form is:

66004 = 2² × 29¹ × 569¹

Step-3: Factors of 66000

List of positive integer factors of 66000 that divides 66000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 100, 110, 120, 125, 132, 150, 165, 176, 200, 220, 240, 250, 264, 275, 300, 330, 375, 400, 440, 500, 528, 550, 600, 660, 750, 825, 880, 1000, 1100, 1200, 1320, 1375, 1500, 1650, 2000, 2200, 2640, 2750, 3000, 3300, 4125, 4400, 5500, 6000, 6600, 8250, 11000, 13200, 16500, 22000, 33000

Step-4: Factors of 66004

List of positive integer factors of 66004 that divides 66000 without a remainder.

1, 2, 4, 29, 58, 116, 569, 1138, 2276, 16501, 33002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66000 and 66004. The biggest common factor number is the GCF number.
So the greatest common factor 66000 and 66004 is 4.

Also check out the Least Common Multiple of 66000 and 66004