72137284128 has 288 divisors, whose sum is σ = 263580549120. Its totient is φ = 19025072640.

The previous prime is 72137284127. The next prime is 72137284189. The reversal of 72137284128 is 82148273127.

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

It is a super-2 number, since 2×72137284128² (a number of 23 digits) contains 22 as substring.

It is a nude number because it is divisible by every one of its digits.

It is not an unprimeable number, because it can be changed into a prime (72137284123) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 484833 + ... + 615903.

It is an arithmetic number, because the mean of its divisors is an integer number (915210240).

Almost surely, 2^72137284128 is an apocalyptic number.

72137284128 is a gapful number since it is divisible by the number (78) 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 72137284128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131790274560).

72137284128 is an abundant number, since it is smaller than the sum of its proper divisors (191443264992).

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

72137284128 is a wasteful number, since it uses less digits than its factorization.

72137284128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 131117 (or 131096 counting only the distinct ones).

The product of its digits is 301056, while the sum is 45.

The spelling of 72137284128 in words is "seventy-two billion, one hundred thirty-seven million, two hundred eighty-four thousand, one hundred twenty-eight".