What is the Greatest Common Factor of 36465 and 36480?

Greatest common factor (GCF) of 36465 and 36480 is 15.

GCF(36465,36480) = 15

We will now calculate the prime factors of 36465 and 36480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36465 and 36480.

How to find the GCF of 36465 and 36480?

We will first find the prime factorization of 36465 and 36480. After we will calculate the factors of 36465 and 36480 and find the biggest common factor number .

Step-1: Prime Factorization of 36465

Prime factors of 36465 are 3, 5, 11, 13, 17. Prime factorization of 36465 in exponential form is:

36465 = 3¹ × 5¹ × 11¹ × 13¹ × 17¹

Step-2: Prime Factorization of 36480

Prime factors of 36480 are 2, 3, 5, 19. Prime factorization of 36480 in exponential form is:

36480 = 2⁷ × 3¹ × 5¹ × 19¹

Step-3: Factors of 36465

List of positive integer factors of 36465 that divides 36465 without a remainder.

1, 3, 5, 11, 13, 15, 17, 33, 39, 51, 55, 65, 85, 143, 165, 187, 195, 221, 255, 429, 561, 663, 715, 935, 1105, 2145, 2431, 2805, 3315, 7293, 12155

Step-4: Factors of 36480

List of positive integer factors of 36480 that divides 36465 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 64, 76, 80, 95, 96, 114, 120, 128, 152, 160, 190, 192, 228, 240, 285, 304, 320, 380, 384, 456, 480, 570, 608, 640, 760, 912, 960, 1140, 1216, 1520, 1824, 1920, 2280, 2432, 3040, 3648, 4560, 6080, 7296, 9120, 12160, 18240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36465 and 36480. The biggest common factor number is the GCF number.
So the greatest common factor 36465 and 36480 is 15.

Also check out the Least Common Multiple of 36465 and 36480