106732800 has 324 divisors, whose sum is σ = 407747340. Its totient is φ = 26542080.

The previous prime is 106732793. The next prime is 106732819. The reversal of 106732800 is 8237601.

It can be written as a sum of positive squares in 6 ways, for example, as 1218816 + 105513984 = 1104^2 + 10272^2 .

It is a super-2 number, since 2×106732800² = 22783781191680000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

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 35 ways as a sum of consecutive naturals, for example, 979146 + ... + 979254.

Almost surely, 2^106732800 is an apocalyptic number.

106732800 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 106732800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (203873670).

106732800 is an abundant number, since it is smaller than the sum of its proper divisors (301014540).

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

106732800 is a wasteful number, since it uses less digits than its factorization.

106732800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 158 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 106732800 is about 10331.1567600148. The cubic root of 106732800 is about 474.3504325209.

The spelling of 106732800 in words is "one hundred six million, seven hundred thirty-two thousand, eight hundred".