72846144 has 252 divisors, whose sum is σ = 254088900. Its totient is φ = 19869696.

The previous prime is 72846121. The next prime is 72846157. The reversal of 72846144 is 44164827.

It can be written as a sum of positive squares in 2 ways, for example, as 25401600 + 47444544 = 5040^2 + 6888^2 .

It is a tau number, because it is divible by the number of its divisors (252).

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.

It is a junction number, because it is equal to n+sod(n) for n = 72846099 and 72846108.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 818452 + ... + 818540.

Almost surely, 2^72846144 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 72846144, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (127044450).

72846144 is an abundant number, since it is smaller than the sum of its proper divisors (181242756).

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

72846144 is a wasteful number, since it uses less digits than its factorization.

72846144 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 150 (or 130 counting only the distinct ones).

The product of its digits is 43008, while the sum is 36.

The square root of 72846144 is about 8534.9952548317. The cubic root of 72846144 is about 417.6400983207.

The spelling of 72846144 in words is "seventy-two million, eight hundred forty-six thousand, one hundred forty-four".