72914400 has 432 divisors, whose sum is σ = 298574640. Its totient is φ = 16588800.

The previous prime is 72914399. The next prime is 72914431. The reversal of 72914400 is 441927.

72914400 = 100³ + 101³ + ... + 140³.

It is a happy number.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1778380 + ... + 1778420.

It is an arithmetic number, because the mean of its divisors is an integer number (691145).

Almost surely, 2^72914400 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 72914400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149287320).

72914400 is an abundant number, since it is smaller than the sum of its proper divisors (225660240).

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

72914400 is a wasteful number, since it uses less digits than its factorization.

72914400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 99 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 72914400 is about 8538.9929148583. The cubic root of 72914400 is about 417.7704989259.

It can be divided in two parts, 729 and 14400, that multiplied together give a square (10497600 = 3240²).

The spelling of 72914400 in words is "seventy-two million, nine hundred fourteen thousand, four hundred".