406778400 has 324 divisors, whose sum is σ = 1670037642. Its totient is φ = 92897280.

The previous prime is 406778341. The next prime is 406778413. The reversal of 406778400 is 4877604.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 350887824 + 55890576 = 18732^2 + 7476^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 352224 + ... + 353376.

Almost surely, 2^406778400 is an apocalyptic number.

406778400 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 406778400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (835018821).

406778400 is an abundant number, since it is smaller than the sum of its proper divisors (1263259242).

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

406778400 is a wasteful number, since it uses less digits than its factorization.

406778400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1193 (or 1170 counting only the distinct ones).

The product of its (nonzero) digits is 37632, while the sum is 36.

The square root of 406778400 is about 20168.7481019522. The cubic root of 406778400 is about 740.9449821740.

The spelling of 406778400 in words is "four hundred six million, seven hundred seventy-eight thousand, four hundred".