72535680 has 288 divisors, whose sum is σ = 292502340. Its totient is φ = 16515072.

The previous prime is 72535679. The next prime is 72535703. The reversal of 72535680 is 8653527.

It can be written as a sum of positive squares in 2 ways, for example, as 67765824 + 4769856 = 8232^2 + 2184^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×72535680² = 10522849746124800, which contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 282112 + ... + 282368.

Almost surely, 2^72535680 is an apocalyptic number.

72535680 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 72535680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146251170).

72535680 is an abundant number, since it is smaller than the sum of its proper divisors (219966660).

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

72535680 is a wasteful number, since it uses less digits than its factorization.

72535680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 296 (or 274 counting only the distinct ones).

The product of its (nonzero) digits is 50400, while the sum is 36.

The square root of 72535680 is about 8516.7881269878. The cubic root of 72535680 is about 417.0459380408.

The spelling of 72535680 in words is "seventy-two million, five hundred thirty-five thousand, six hundred eighty".