What is the Greatest Common Factor of 66000 and 66005?

Greatest common factor (GCF) of 66000 and 66005 is 5.

GCF(66000,66005) = 5

We will now calculate the prime factors of 66000 and 66005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66000 and 66005.

How to find the GCF of 66000 and 66005?

We will first find the prime factorization of 66000 and 66005. After we will calculate the factors of 66000 and 66005 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 66005

Prime factors of 66005 are 5, 43, 307. Prime factorization of 66005 in exponential form is:

66005 = 5¹ × 43¹ × 307¹

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 66005

List of positive integer factors of 66005 that divides 66000 without a remainder.

1, 5, 43, 215, 307, 1535, 13201

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66000 and 66005. The biggest common factor number is the GCF number.
So the greatest common factor 66000 and 66005 is 5.

Also check out the Least Common Multiple of 66000 and 66005