414097920 has 200 divisors, whose sum is σ = 1483910604. Its totient is φ = 110370816.

The previous prime is 414097919. The next prime is 414097927. The reversal of 414097920 is 29790414.

It can be written as a sum of positive squares in 2 ways, for example, as 355850496 + 58247424 = 18864^2 + 7632^2 .

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (414097927) by changing a digit.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 206362 + ... + 208358.

Almost surely, 2^414097920 is an apocalyptic number.

414097920 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 414097920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (741955302).

414097920 is an abundant number, since it is smaller than the sum of its proper divisors (1069812684).

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

414097920 is an equidigital number, since it uses as much as digits as its factorization.

414097920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2032 (or 2007 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 36.

The square root of 414097920 is about 20349.3960598343. The cubic root of 414097920 is about 745.3627469387.

The spelling of 414097920 in words is "four hundred fourteen million, ninety-seven thousand, nine hundred twenty".