414242400 has 576 divisors, whose sum is σ = 1700891136. Its totient is φ = 86016000.

The previous prime is 414242371. The next prime is 414242407. The reversal of 414242400 is 4242414.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414242407) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 5834365 + ... + 5834435.

It is an arithmetic number, because the mean of its divisors is an integer number (2952936).

Almost surely, 2^414242400 is an apocalyptic number.

414242400 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 414242400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (850445568).

414242400 is an abundant number, since it is smaller than the sum of its proper divisors (1286648736).

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

414242400 is a wasteful number, since it uses less digits than its factorization.

414242400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 135 (or 122 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 21.

The square root of 414242400 is about 20352.9457327435. The cubic root of 414242400 is about 745.4494232879.

Adding to 414242400 its reverse (4242414), we get a palindrome (418484814).

The spelling of 414242400 in words is "four hundred fourteen million, two hundred forty-two thousand, four hundred".