72867600 has 300 divisors, whose sum is σ = 283260516. Its totient is φ = 17832960.

The previous prime is 72867589. The next prime is 72867601. The reversal of 72867600 is 676827.

It can be written as a sum of positive squares in 6 ways, for example, as 685584 + 72182016 = 828^2 + 8496^2 .

It is a tau number, because it is divible by the number of its divisors (300).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72867601) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 421114 + ... + 421286.

Almost surely, 2^72867600 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 72867600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (141630258).

72867600 is an abundant number, since it is smaller than the sum of its proper divisors (210392916).

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

72867600 is a wasteful number, since it uses less digits than its factorization.

72867600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 216 (or 196 counting only the distinct ones).

The product of its (nonzero) digits is 28224, while the sum is 36.

The square root of 72867600 is about 8536.2521049932. The cubic root of 72867600 is about 417.6810980032.

The spelling of 72867600 in words is "seventy-two million, eight hundred sixty-seven thousand, six hundred".