72735600 has 180 divisors, whose sum is σ = 271255704. Its totient is φ = 16611840.

The previous prime is 72735589. The next prime is 72735647. The reversal of 72735600 is 653727.

It is a hoax number, since the sum of its digits (30) coincides with the sum of the digits of its distinct prime factors.

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 35 ways as a sum of consecutive naturals, for example, 58182 + ... + 59418.

Almost surely, 2^72735600 is an apocalyptic number.

72735600 is a gapful number since it is divisible by the number (70) 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 72735600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (135627852).

72735600 is an abundant number, since it is smaller than the sum of its proper divisors (198520104).

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

72735600 is a wasteful number, since it uses less digits than its factorization.

72735600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1272 (or 1254 counting only the distinct ones).

The product of its (nonzero) digits is 8820, while the sum is 30.

The square root of 72735600 is about 8528.5168698901. The cubic root of 72735600 is about 417.4287351320.

The spelling of 72735600 in words is "seventy-two million, seven hundred thirty-five thousand, six hundred".