72950400 has 288 divisors, whose sum is σ = 277465500. Its totient is φ = 18186240.

The previous prime is 72950387. The next prime is 72950401. The reversal of 72950400 is 405927.

It can be written as a sum of positive squares in 6 ways, for example, as 21455424 + 51494976 = 4632^2 + 7176^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72950401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 489526 + ... + 489674.

Almost surely, 2^72950400 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 72950400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138732750).

72950400 is an abundant number, since it is smaller than the sum of its proper divisors (204515100).

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

72950400 is a wasteful number, since it uses less digits than its factorization.

72950400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 196 (or 176 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 72950400 is about 8541.1006316516. The cubic root of 72950400 is about 417.8392428386.

The spelling of 72950400 in words is "seventy-two million, nine hundred fifty thousand, four hundred".