72972900 has 504 divisors, whose sum is σ = 318771264. Its totient is φ = 13996800.

The previous prime is 72972883. The next prime is 72972919. The reversal of 72972900 is 927927.

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 5613294 + ... + 5613306.

Almost surely, 2^72972900 is an apocalyptic number.

72972900 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 72972900, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (159385632).

72972900 is an abundant number, since it is smaller than the sum of its proper divisors (245798364).

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

72972900 is a wasteful number, since it uses less digits than its factorization.

72972900 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 63 (or 41 counting only the distinct ones).

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

The square root of 72972900 is about 8542.4176905604. The cubic root of 72972900 is about 417.8821963000.

It can be divided in two parts, 729 and 72900, that multiplied together give a square (53144100 = 7290²).

The spelling of 72972900 in words is "seventy-two million, nine hundred seventy-two thousand, nine hundred".