414130400 has 72 divisors (see below), whose sum is σ = 1013841360. Its totient is φ = 165186560.

The previous prime is 414130397. The next prime is 414130447. The reversal of 414130400 is 4031414.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 493181 + ... + 494019.

It is an arithmetic number, because the mean of its divisors is an integer number (14081130).

Almost surely, 2^414130400 is an apocalyptic number.

414130400 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 414130400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (506920680).

414130400 is an abundant number, since it is smaller than the sum of its proper divisors (599710960).

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

414130400 is a wasteful number, since it uses less digits than its factorization.

414130400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1476 (or 1463 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 17.

The square root of 414130400 is about 20350.1941022684. The cubic root of 414130400 is about 745.3822340761.

Adding to 414130400 its reverse (4031414), we get a palindrome (418161814).

The spelling of 414130400 in words is "four hundred fourteen million, one hundred thirty thousand, four hundred".