72612000 has 144 divisors (see below), whose sum is σ = 257827752. Its totient is φ = 19353600.

The previous prime is 72611999. The next prime is 72612017. The reversal of 72612000 is 21627.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 34715664 + 37896336 = 5892^2 + 6156^2 .

It is a tau number, because it is divible by the number of its divisors (144).

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

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 34992 + ... + 37008.

Almost surely, 2^72612000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72612000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (128913876).

72612000 is an abundant number, since it is smaller than the sum of its proper divisors (185215752).

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

72612000 is a wasteful number, since it uses less digits than its factorization.

72612000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2048 (or 2027 counting only the distinct ones).

The product of its (nonzero) digits is 168, while the sum is 18.

The square root of 72612000 is about 8521.2675113506. The cubic root of 72612000 is about 417.1921547686.

Adding to 72612000 its reverse (21627), we get a palindrome (72633627).

It can be divided in two parts, 7261 and 2000, that added together give a cube (9261 = 21³).

The spelling of 72612000 in words is "seventy-two million, six hundred twelve thousand".