What is the Greatest Common Factor of 90720 and 90729?

Greatest common factor (GCF) of 90720 and 90729 is 9.

GCF(90720,90729) = 9

We will now calculate the prime factors of 90720 and 90729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90720 and 90729.

How to find the GCF of 90720 and 90729?

We will first find the prime factorization of 90720 and 90729. After we will calculate the factors of 90720 and 90729 and find the biggest common factor number .

Step-1: Prime Factorization of 90720

Prime factors of 90720 are 2, 3, 5, 7. Prime factorization of 90720 in exponential form is:

90720 = 2⁵ × 3⁴ × 5¹ × 7¹

Step-2: Prime Factorization of 90729

Prime factors of 90729 are 3, 17, 593. Prime factorization of 90729 in exponential form is:

90729 = 3² × 17¹ × 593¹

Step-3: Factors of 90720

List of positive integer factors of 90720 that divides 90720 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 81, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 162, 168, 180, 189, 210, 216, 224, 240, 252, 270, 280, 288, 315, 324, 336, 360, 378, 405, 420, 432, 480, 504, 540, 560, 567, 630, 648, 672, 720, 756, 810, 840, 864, 945, 1008, 1080, 1120, 1134, 1260, 1296, 1440, 1512, 1620, 1680, 1890, 2016, 2160, 2268, 2520, 2592, 2835, 3024, 3240, 3360, 3780, 4320, 4536, 5040, 5670, 6048, 6480, 7560, 9072, 10080, 11340, 12960, 15120, 18144, 22680, 30240, 45360

Step-4: Factors of 90729

List of positive integer factors of 90729 that divides 90720 without a remainder.

1, 3, 9, 17, 51, 153, 593, 1779, 5337, 10081, 30243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90720 and 90729. The biggest common factor number is the GCF number.
So the greatest common factor 90720 and 90729 is 9.

Also check out the Least Common Multiple of 90720 and 90729