106782371735040 has 960 divisors, whose sum is σ = 396685210521600. Its totient is φ = 26468383260672.

The previous prime is 106782371734901. The next prime is 106782371735047. The reversal of 106782371735040 is 40537173287601.

106782371735040 is a `hidden beast` number, since 1 + 0 + 6 + 7 + 8 + 237 + 17 + 350 + 40 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a super-2 number, since 2×106782371735040² (a number of 29 digits) contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (106782371735047) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 4914720657 + ... + 4914742383.

It is an arithmetic number, because the mean of its divisors is an integer number (413213760960).

Almost surely, 2^{106782371735040} is an apocalyptic number.

106782371735040 is a gapful number since it is divisible by the number (10) 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 106782371735040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (198342605260800).

106782371735040 is an abundant number, since it is smaller than the sum of its proper divisors (289902838786560).

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

106782371735040 is a wasteful number, since it uses less digits than its factorization.

106782371735040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 21987 (or 21968 counting only the distinct ones).

The product of its (nonzero) digits is 5927040, while the sum is 54.

The spelling of 106782371735040 in words is "one hundred six trillion, seven hundred eighty-two billion, three hundred seventy-one million, seven hundred thirty-five thousand, forty".