414268400 has 240 divisors, whose sum is σ = 1291584000. Its totient is φ = 124001280.

The previous prime is 414268397. The next prime is 414268423. The reversal of 414268400 is 4862414.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 691301 + ... + 691899.

It is an arithmetic number, because the mean of its divisors is an integer number (5381600).

Almost surely, 2^414268400 is an apocalyptic number.

414268400 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 414268400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (645792000).

414268400 is an abundant number, since it is smaller than the sum of its proper divisors (877315600).

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

414268400 is a wasteful number, since it uses less digits than its factorization.

414268400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 656 (or 645 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 29.

The square root of 414268400 is about 20353.5844509020. The cubic root of 414268400 is about 745.4650190514.

The spelling of 414268400 in words is "four hundred fourteen million, two hundred sixty-eight thousand, four hundred".