45360 has 100 divisors (see below), whose sum is σ = 180048. Its totient is φ = 10368.

The previous prime is 45343. The next prime is 45361. The reversal of 45360 is 6354.

45360 = 21² + 22² + ... + 52².

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 45360.

It is not an unprimeable number, because it can be changed into a prime (45361) by changing a digit.

45360 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 6477 + ... + 6483.

45360 is a Friedman number, since it can be written as 35*(6+0)^4, using all its digits and the basic arithmetic operations.

45360 is a highly composite number, because it has more divisors than any smaller number.

2⁴⁵³⁶⁰ is an apocalyptic number.

45360 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

45360 is the 135-th heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 45360, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (90024).

45360 is an abundant number, since it is smaller than the sum of its proper divisors (134688).

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

45360 is a wasteful number, since it uses less digits than its factorization.

45360 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 360, while the sum is 18.

The square root of 45360 is about 212.9788721916. The cubic root of 45360 is about 35.6635317166.

The spelling of 45360 in words is "forty-five thousand, three hundred sixty".