72712400 has 120 divisors (see below), whose sum is σ = 190623960. Its totient is φ = 26634240.

The previous prime is 72712397. The next prime is 72712421. The reversal of 72712400 is 421727.

It can be written as a sum of positive squares in 12 ways, for example, as 4682896 + 68029504 = 2164^2 + 8248^2 .

It is a super-2 number, since 2×72712400² = 10574186227520000, which contains 22 as substring.

It is a congruent number.

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, 1965182 + ... + 1965218.

It is an arithmetic number, because the mean of its divisors is an integer number (1588533).

Almost surely, 2^72712400 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 72712400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (95311980).

72712400 is an abundant number, since it is smaller than the sum of its proper divisors (117911560).

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

72712400 is a wasteful number, since it uses less digits than its factorization.

72712400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 106 (or 61 counting only the distinct ones).

The product of its (nonzero) digits is 784, while the sum is 23.

The square root of 72712400 is about 8527.1566187094. The cubic root of 72712400 is about 417.3843489053.

The spelling of 72712400 in words is "seventy-two million, seven hundred twelve thousand, four hundred".