106767410400 has 864 divisors, whose sum is σ = 440554802688. Its totient is φ = 23829811200.

The previous prime is 106767410377. The next prime is 106767410411. The reversal of 106767410400 is 4014767601.

106767410400 is a `hidden beast` number, since 106 + 76 + 74 + 10 + 400 = 666.

It is a super-2 number, since 2×106767410400² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 680047122 + ... + 680047278.

It is an arithmetic number, because the mean of its divisors is an integer number (509901392).

Almost surely, 2^106767410400 is an apocalyptic number.

106767410400 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 106767410400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (220277401344).

106767410400 is an abundant number, since it is smaller than the sum of its proper divisors (333787392288).

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

106767410400 is a wasteful number, since it uses less digits than its factorization.

106767410400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 424 (or 408 counting only the distinct ones).

The product of its (nonzero) digits is 28224, while the sum is 36.

The spelling of 106767410400 in words is "one hundred six billion, seven hundred sixty-seven million, four hundred ten thousand, four hundred".