106638400 has 168 divisors, whose sum is σ = 293668704. Its totient is φ = 37785600.

The previous prime is 106638397. The next prime is 106638401. The reversal of 106638400 is 4836601.

It is a super-3 number, since 3×106638400³ (a number of 25 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is not an unprimeable number, because it can be changed into a prime (106638401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1284759 + ... + 1284841.

It is an arithmetic number, because the mean of its divisors is an integer number (1748028).

Almost surely, 2^106638400 is an apocalyptic number.

106638400 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 106638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146834352).

106638400 is an abundant number, since it is smaller than the sum of its proper divisors (187030304).

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

106638400 is a wasteful number, since it uses less digits than its factorization.

106638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 189 (or 174 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 28.

The square root of 106638400 is about 10326.5870450987. The cubic root of 106638400 is about 474.2105445987.

The spelling of 106638400 in words is "one hundred six million, six hundred thirty-eight thousand, four hundred".