72738000 has 200 divisors, whose sum is σ = 263320200. Its totient is φ = 19353600.

The previous prime is 72737993. The next prime is 72738007. The reversal of 72738000 is 83727.

It is an interprime number because it is at equal distance from previous prime (72737993) and next prime (72738007).

It can be written as a sum of positive squares in 4 ways, for example, as 1774224 + 70963776 = 1332^2 + 8424^2 .

It is a tau number, because it is divible by the number of its divisors (200).

It is a hoax number, since the sum of its digits (27) 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 (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72738007) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 161776 + ... + 162224.

It is an arithmetic number, because the mean of its divisors is an integer number (1316601).

Almost surely, 2^72738000 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 72738000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131660100).

72738000 is an abundant number, since it is smaller than the sum of its proper divisors (190582200).

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

72738000 is a wasteful number, since it uses less digits than its factorization.

72738000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 484 (or 459 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 72738000 is about 8528.6575731471. The cubic root of 72738000 is about 417.4333262719.

The spelling of 72738000 in words is "seventy-two million, seven hundred thirty-eight thousand".