72993312 has 192 divisors, whose sum is σ = 247968000. Its totient is φ = 20715264.

The previous prime is 72993311. The next prime is 72993353. The reversal of 72993312 is 21339927.

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

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is not an unprimeable number, because it can be changed into a prime (72993311) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 489814 + ... + 489962.

It is an arithmetic number, because the mean of its divisors is an integer number (1291500).

Almost surely, 2^72993312 is an apocalyptic number.

72993312 is a gapful number since it is divisible by the number (72) 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 72993312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (123984000).

72993312 is an abundant number, since it is smaller than the sum of its proper divisors (174974688).

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

72993312 is an equidigital number, since it uses as much as digits as its factorization.

72993312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 187 (or 161 counting only the distinct ones).

The product of its digits is 20412, while the sum is 36.

The square root of 72993312 is about 8543.6123507566. The cubic root of 72993312 is about 417.9211560426.

The spelling of 72993312 in words is "seventy-two million, nine hundred ninety-three thousand, three hundred twelve".