414400000 has 240 divisors, whose sum is σ = 1214734752. Its totient is φ = 138240000.

The previous prime is 414399977. The next prime is 414400001. The reversal of 414400000 is 4414.

It is a happy number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414400001) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 11199982 + ... + 11200018.

Almost surely, 2^414400000 is an apocalyptic number.

414400000 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 414400000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (607367376).

414400000 is an abundant number, since it is smaller than the sum of its proper divisors (800334752).

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

414400000 is an frugal number, since it uses more digits than its factorization.

414400000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 87 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 13.

The square root of 414400000 is about 20356.8170399992. The cubic root of 414400000 is about 745.5439475997.

Adding to 414400000 its reverse (4414), we get a palindrome (414404414).

The spelling of 414400000 in words is "four hundred fourteen million, four hundred thousand".