45768000 has 112 divisors (see below), whose sum is σ = 151205184. Its totient is φ = 12198400.

The previous prime is 45767977. The next prime is 45768043. The reversal of 45768000 is 86754.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 23047 + ... + 24953.

Almost surely, 2^45768000 is an apocalyptic number.

45768000 is a gapful number since it is divisible by the number (40) 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 45768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (75602592).

45768000 is an abundant number, since it is smaller than the sum of its proper divisors (105437184).

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

45768000 is a wasteful number, since it uses less digits than its factorization.

45768000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1937 (or 1917 counting only the distinct ones).

The product of its (nonzero) digits is 6720, while the sum is 30.

The square root of 45768000 is about 6765.2050966693. The cubic root of 45768000 is about 357.7014041107.

The spelling of 45768000 in words is "forty-five million, seven hundred sixty-eight thousand".