72979200 has 324 divisors, whose sum is σ = 299838448. Its totient is φ = 16588800.

The previous prime is 72979189. The next prime is 72979201. The reversal of 72979200 is 297927.

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

It is not an unprimeable number, because it can be changed into a prime (72979201) 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, 403110 + ... + 403290.

Almost surely, 2^72979200 is an apocalyptic number.

72979200 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 72979200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149919224).

72979200 is an abundant number, since it is smaller than the sum of its proper divisors (226859248).

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

72979200 is a wasteful number, since it uses less digits than its factorization.

72979200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 220 (or 198 counting only the distinct ones).

The product of its (nonzero) digits is 15876, while the sum is 36.

The square root of 72979200 is about 8542.7864306677. The cubic root of 72979200 is about 417.8942216870.

The spelling of 72979200 in words is "seventy-two million, nine hundred seventy-nine thousand, two hundred".