414200010400 has 288 divisors, whose sum is σ = 1117679713920. Its totient is φ = 148635648000.

The previous prime is 414200010397. The next prime is 414200010403. The reversal of 414200010400 is 4010002414.

It is an interprime number because it is at equal distance from previous prime (414200010397) and next prime (414200010403).

It is a Harshad number since it is a multiple of its sum of digits (16).

It is not an unprimeable number, because it can be changed into a prime (414200010403) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 538621216 + ... + 538621984.

It is an arithmetic number, because the mean of its divisors is an integer number (3880832340).

Almost surely, 2^414200010400 is an apocalyptic number.

414200010400 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 414200010400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (558839856960).

414200010400 is an abundant number, since it is smaller than the sum of its proper divisors (703479703520).

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

414200010400 is a wasteful number, since it uses less digits than its factorization.

414200010400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1528 (or 1515 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 16.

Adding to 414200010400 its reverse (4010002414), we get a palindrome (418210012814).

The spelling of 414200010400 in words is "four hundred fourteen billion, two hundred million, ten thousand, four hundred".