414509040 has 240 divisors, whose sum is σ = 1532044800. Its totient is φ = 99601920.

The previous prime is 414509003. The next prime is 414509063. The reversal of 414509040 is 40905414.

It is a tau number, because it is divible by the number of its divisors (240).

It is a junction number, because it is equal to n+sod(n) for n = 414508995 and 414509013.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1575949 + ... + 1576211.

It is an arithmetic number, because the mean of its divisors is an integer number (6383520).

Almost surely, 2^414509040 is an apocalyptic number.

414509040 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 414509040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (766022400).

414509040 is an abundant number, since it is smaller than the sum of its proper divisors (1117535760).

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

414509040 is a wasteful number, since it uses less digits than its factorization.

414509040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 492 (or 483 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 414509040 is about 20359.4950821478. The cubic root of 414509040 is about 745.6093328819.

The spelling of 414509040 in words is "four hundred fourteen million, five hundred nine thousand, forty".