414040320 has 216 divisors, whose sum is σ = 1448918016. Its totient is φ = 109154304.

The previous prime is 414040307. The next prime is 414040331. The reversal of 414040320 is 23040414.

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

It is a junction number, because it is equal to n+sod(n) for n = 414040293 and 414040302.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1462899 + ... + 1463181.

Almost surely, 2^414040320 is an apocalyptic number.

414040320 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 414040320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (724459008).

414040320 is an abundant number, since it is smaller than the sum of its proper divisors (1034877696).

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

414040320 is a wasteful number, since it uses less digits than its factorization.

414040320 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 437 (or 420 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 18.

The square root of 414040320 is about 20347.9807351983. The cubic root of 414040320 is about 745.3281859626.

Adding to 414040320 its reverse (23040414), we get a palindrome (437080734).

The spelling of 414040320 in words is "four hundred fourteen million, forty thousand, three hundred twenty".