72717840 has 240 divisors, whose sum is σ = 279075888. Its totient is φ = 16809984.

The previous prime is 72717829. The next prime is 72717851. The reversal of 72717840 is 4871727.

It is an interprime number because it is at equal distance from previous prime (72717829) and next prime (72717851).

It can be written as a sum of positive squares in 8 ways, for example, as 535824 + 72182016 = 732^2 + 8496^2 .

It is a tau number, because it is divible by the number of its divisors (240).

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

It is a junction number, because it is equal to n+sod(n) for n = 72717795 and 72717804.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 158892 + ... + 159348.

Almost surely, 2^72717840 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 72717840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (139537944).

72717840 is an abundant number, since it is smaller than the sum of its proper divisors (206358048).

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

72717840 is a wasteful number, since it uses less digits than its factorization.

72717840 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 506 (or 497 counting only the distinct ones).

The product of its (nonzero) digits is 21952, while the sum is 36.

The square root of 72717840 is about 8527.4755936326. The cubic root of 72717840 is about 417.3947575575.

The spelling of 72717840 in words is "seventy-two million, seven hundred seventeen thousand, eight hundred forty".