What is the Greatest Common Factor of 81600 and 81609?

Greatest common factor (GCF) of 81600 and 81609 is 3.

GCF(81600,81609) = 3

We will now calculate the prime factors of 81600 and 81609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81600 and 81609.

How to find the GCF of 81600 and 81609?

We will first find the prime factorization of 81600 and 81609. After we will calculate the factors of 81600 and 81609 and find the biggest common factor number .

Step-1: Prime Factorization of 81600

Prime factors of 81600 are 2, 3, 5, 17. Prime factorization of 81600 in exponential form is:

81600 = 2⁶ × 3¹ × 5² × 17¹

Step-2: Prime Factorization of 81609

Prime factors of 81609 are 3, 11, 2473. Prime factorization of 81609 in exponential form is:

81609 = 3¹ × 11¹ × 2473¹

Step-3: Factors of 81600

List of positive integer factors of 81600 that divides 81600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 32, 34, 40, 48, 50, 51, 60, 64, 68, 75, 80, 85, 96, 100, 102, 120, 136, 150, 160, 170, 192, 200, 204, 240, 255, 272, 300, 320, 340, 400, 408, 425, 480, 510, 544, 600, 680, 800, 816, 850, 960, 1020, 1088, 1200, 1275, 1360, 1600, 1632, 1700, 2040, 2400, 2550, 2720, 3264, 3400, 4080, 4800, 5100, 5440, 6800, 8160, 10200, 13600, 16320, 20400, 27200, 40800

Step-4: Factors of 81609

List of positive integer factors of 81609 that divides 81600 without a remainder.

1, 3, 11, 33, 2473, 7419, 27203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81600 and 81609. The biggest common factor number is the GCF number.
So the greatest common factor 81600 and 81609 is 3.

Also check out the Least Common Multiple of 81600 and 81609