4112800 has 72 divisors (see below), whose sum is σ = 10335276. Its totient is φ = 1597440.

The previous prime is 4112777. The next prime is 4112807. The reversal of 4112800 is 82114.

4112800 = 156² + 157² + ... + 252².

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 1838736 + 2274064 = 1356^2 + 1508^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is not an unprimeable number, because it can be changed into a prime (4112807) 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, 42352 + ... + 42448.

Almost surely, 2^4112800 is an apocalyptic number.

4112800 is a gapful number since it is divisible by the number (40) 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 4112800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5167638).

4112800 is an abundant number, since it is smaller than the sum of its proper divisors (6222476).

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

4112800 is a wasteful number, since it uses less digits than its factorization.

4112800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 170 (or 157 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 16.

The square root of 4112800 is about 2028.0039447693. The cubic root of 4112800 is about 160.2184516074.

Subtracting from 4112800 its sum of digits (16), we obtain a square (4112784 = 2028²).

Adding to 4112800 its reverse (82114), we get a palindrome (4194914).

It can be divided in two parts, 41 and 12800, that multiplied together give a triangular number (524800 = T₁₀₂₄).

The spelling of 4112800 in words is "four million, one hundred twelve thousand, eight hundred".