106838400 has 192 divisors, whose sum is σ = 364262400. Its totient is φ = 27494400.

The previous prime is 106838383. The next prime is 106838423. The reversal of 106838400 is 4838601.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-2 number, since 2×106838400² = 22828887429120000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 297421 + ... + 297779.

It is an arithmetic number, because the mean of its divisors is an integer number (1897200).

Almost surely, 2^106838400 is an apocalyptic number.

106838400 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 106838400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (182131200).

106838400 is an abundant number, since it is smaller than the sum of its proper divisors (257424000).

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

106838400 is a wasteful number, since it uses less digits than its factorization.

106838400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 417 (or 400 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 30.

The square root of 106838400 is about 10336.2662504407. The cubic root of 106838400 is about 474.5068196072.

The spelling of 106838400 in words is "one hundred six million, eight hundred thirty-eight thousand, four hundred".