112417617312 has 1152 divisors, whose sum is σ = 463325184000. Its totient is φ = 26040268800.

The previous prime is 112417617287. The next prime is 112417617313. The reversal of 112417617312 is 213716714211.

112417617312 is a `hidden beast` number, since 1 + 1 + 2 + 4 + 1 + 7 + 617 + 31 + 2 = 666.

112417617312 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

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 and also a Zuckerman number because it is divisible by the product of its digits.

It is not an unprimeable number, because it can be changed into a prime (112417617313) 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 191 ways as a sum of consecutive naturals, for example, 187675189 + ... + 187675787.

It is an arithmetic number, because the mean of its divisors is an integer number (402192000).

Almost surely, 2^112417617312 is an apocalyptic number.

112417617312 is a gapful number since it is divisible by the number (12) 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 112417617312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (231662592000).

112417617312 is an abundant number, since it is smaller than the sum of its proper divisors (350907566688).

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

112417617312 is a wasteful number, since it uses less digits than its factorization.

112417617312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 687 (or 666 counting only the distinct ones).

The product of its digits is 14112, while the sum is 36.

The spelling of 112417617312 in words is "one hundred twelve billion, four hundred seventeen million, six hundred seventeen thousand, three hundred twelve".