4006400 has 60 divisors (see below), whose sum is σ = 9957882. Its totient is φ = 1597440.

The previous prime is 4006381. The next prime is 4006403. The reversal of 4006400 is 46004.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 1597696 + 2408704 = 1264^2 + 1552^2 .

It is a hoax number, since the sum of its digits (14) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (4006403) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 12644 + ... + 12956.

Almost surely, 2^4006400 is an apocalyptic number.

4006400 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 4006400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4978941).

4006400 is an abundant number, since it is smaller than the sum of its proper divisors (5951482).

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

4006400 is an equidigital number, since it uses as much as digits as its factorization.

4006400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 341 (or 320 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 14.

The square root of 4006400 is about 2001.5993605115. The cubic root of 4006400 is about 158.8247214736.

It can be divided in two parts, 400 and 6400, that multiplied together give a 4-th power (2560000 = 40⁴).

The spelling of 4006400 in words is "four million, six thousand, four hundred".