414140400 has 360 divisors, whose sum is σ = 1559726064. Its totient is φ = 101376000.

The previous prime is 414140399. The next prime is 414140401. The reversal of 414140400 is 4041414.

It is an interprime number because it is at equal distance from previous prime (414140399) and next prime (414140401).

It is a tau number, because it is divible by the number of its divisors (360).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414140401) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 4100350 + ... + 4100450.

Almost surely, 2^414140400 is an apocalyptic number.

414140400 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 414140400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (779863032).

414140400 is an abundant number, since it is smaller than the sum of its proper divisors (1145585664).

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

414140400 is a wasteful number, since it uses less digits than its factorization.

414140400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 209 (or 195 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 18.

The square root of 414140400 is about 20350.4397986874. The cubic root of 414140400 is about 745.3882336053.

Adding to 414140400 its reverse (4041414), we get a palindrome (418181814).

The spelling of 414140400 in words is "four hundred fourteen million, one hundred forty thousand, four hundred".