106800 has 60 divisors (see below), whose sum is σ = 345960. Its totient is φ = 28160.

The previous prime is 106787. The next prime is 106801. The reversal of 106800 is 8601.

It is a tau number, because it is divible by the number of its divisors (60).

It is a super-2 number, since 2×106800² = 22812480000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 106800.

It is not an unprimeable number, because it can be changed into a prime (106801) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1156 + ... + 1244.

It is an arithmetic number, because the mean of its divisors is an integer number (5766).

2¹⁰⁶⁸⁰⁰ is an apocalyptic number.

106800 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

106800 is the 267-th pentagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 106800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (172980).

106800 is an abundant number, since it is smaller than the sum of its proper divisors (239160).

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

106800 is a wasteful number, since it uses less digits than its factorization.

With its predecessor (106799) it forms a Ruth-Aaron pair, since the sum of their prime factors is the same (110).

106800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 110 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 15.

The square root of 106800 is about 326.8026927674. The cubic root of 106800 is about 47.4449963504. Note that the first 3 decimals are identical.

The spelling of 106800 in words is "one hundred six thousand, eight hundred".