72124416 has 288 divisors, whose sum is σ = 262342080. Its totient is φ = 18579456.

The previous prime is 72124391. The next prime is 72124417. The reversal of 72124416 is 61442127.

72124416 is a `hidden beast` number, since 7 + 212 + 441 + 6 = 666.

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

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 a self number, because there is not a number n which added to its sum of digits gives 72124416.

It is not an unprimeable number, because it can be changed into a prime (72124417) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1677291 + ... + 1677333.

It is an arithmetic number, because the mean of its divisors is an integer number (910910).

Almost surely, 2^72124416 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 72124416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131171040).

72124416 is an abundant number, since it is smaller than the sum of its proper divisors (190217664).

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

72124416 is a wasteful number, since it uses less digits than its factorization.

72124416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 91 (or 68 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 72124416 is about 8492.6094929650. The cubic root of 72124416 is about 416.2562523748.

It can be divided in two parts, 7212 and 4416, that added together give a triangular number (11628 = T₁₅₂).

The spelling of 72124416 in words is "seventy-two million, one hundred twenty-four thousand, four hundred sixteen".