407606400 has 144 divisors (see below), whose sum is σ = 1454535810. Its totient is φ = 108687360.

The previous prime is 407606351. The next prime is 407606401. The reversal of 407606400 is 4606704.

It can be written as a sum of positive squares in 3 ways, for example, as 279825984 + 127780416 = 16728^2 + 11304^2 .

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-2 number, since 2×407606400² = 332285954641920000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (407606401) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 21724 + ... + 35876.

Almost surely, 2^407606400 is an apocalyptic number.

407606400 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 407606400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (727267905).

407606400 is an abundant number, since it is smaller than the sum of its proper divisors (1046929410).

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

407606400 is a wasteful number, since it uses less digits than its factorization.

407606400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 14183 (or 14163 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 27.

The square root of 407606400 is about 20189.2644739723. The cubic root of 407606400 is about 741.4473741829.

The spelling of 407606400 in words is "four hundred seven million, six hundred six thousand, four hundred".