What is the Greatest Common Factor of 90720 and 90735?

Greatest common factor (GCF) of 90720 and 90735 is 15.

GCF(90720,90735) = 15

We will now calculate the prime factors of 90720 and 90735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90720 and 90735.

How to find the GCF of 90720 and 90735?

We will first find the prime factorization of 90720 and 90735. After we will calculate the factors of 90720 and 90735 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 90735

Prime factors of 90735 are 3, 5, 23, 263. Prime factorization of 90735 in exponential form is:

90735 = 3¹ × 5¹ × 23¹ × 263¹

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 90735

List of positive integer factors of 90735 that divides 90720 without a remainder.

1, 3, 5, 15, 23, 69, 115, 263, 345, 789, 1315, 3945, 6049, 18147, 30245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90720 and 90735. The biggest common factor number is the GCF number.
So the greatest common factor 90720 and 90735 is 15.

Also check out the Least Common Multiple of 90720 and 90735