36480 has 64 divisors (see below), whose sum is σ = 122400. Its totient is φ = 9216.

The previous prime is 36479. The next prime is 36493. The reversal of 36480 is 8463.

It is a Cunningham number, because it is equal to 191²-1.

It is a tau number, because it is divible by the number of its divisors (64).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 36480.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1911 + ... + 1929.

2³⁶⁴⁸⁰ is an apocalyptic number.

36480 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 36480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (61200).

36480 is an abundant number, since it is smaller than the sum of its proper divisors (85920).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

36480 is a wasteful number, since it uses less digits than its factorization.

36480 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 41 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 36480 is about 190.9973821810. The cubic root of 36480 is about 33.1653773674.

It can be divided in two parts, 364 and 80, that added together give a palindrome (444).

The spelling of 36480 in words is "thirty-six thousand, four hundred eighty".