72738400 has 144 divisors (see below), whose sum is σ = 209986560. Its totient is φ = 24076800.

The previous prime is 72738389. The next prime is 72738433. The reversal of 72738400 is 483727.

It is a Harshad number since it is a multiple of its sum of digits (31).

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, 173391 + ... + 173809.

It is an arithmetic number, because the mean of its divisors is an integer number (1458240).

Almost surely, 2^72738400 is an apocalyptic number.

72738400 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 72738400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (104993280).

72738400 is an abundant number, since it is smaller than the sum of its proper divisors (137248160).

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

72738400 is a wasteful number, since it uses less digits than its factorization.

72738400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 477 (or 464 counting only the distinct ones).

The product of its (nonzero) digits is 9408, while the sum is 31.

The square root of 72738400 is about 8528.6810234643. The cubic root of 72738400 is about 417.4340914521.

The spelling of 72738400 in words is "seventy-two million, seven hundred thirty-eight thousand, four hundred".