106786252800 has 504 divisors, whose sum is σ = 397105032870. Its totient is φ = 28466380800.

The previous prime is 106786252739. The next prime is 106786252829. The reversal of 106786252800 is 8252687601.

106786252800 is a `hidden beast` number, since 1 + 0 + 67 + 8 + 62 + 528 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 81786848256 + 24999404544 = 285984^2 + 158112^2 .

It is a super-2 number, since 2×106786252800² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 37323370 + ... + 37326230.

Almost surely, 2^106786252800 is an apocalyptic number.

106786252800 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 106786252800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (198552516435).

106786252800 is an abundant number, since it is smaller than the sum of its proper divisors (290318780070).

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

106786252800 is an frugal number, since it uses more digits than its factorization.

106786252800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2911 (or 2871 counting only the distinct ones).

The product of its (nonzero) digits is 322560, while the sum is 45.

The spelling of 106786252800 in words is "one hundred six billion, seven hundred eighty-six million, two hundred fifty-two thousand, eight hundred".