414681120 has 360 divisors, whose sum is σ = 1705021164. Its totient is φ = 94639104.

The previous prime is 414681101. The next prime is 414681131. The reversal of 414681120 is 21186414.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 396328464 + 18352656 = 19908^2 + 4284^2 .

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 (27).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 634714 + ... + 635366.

Almost surely, 2^414681120 is an apocalyptic number.

414681120 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 414681120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (852510582).

414681120 is an abundant number, since it is smaller than the sum of its proper divisors (1290340044).

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

414681120 is a wasteful number, since it uses less digits than its factorization.

414681120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 694 (or 670 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

The square root of 414681120 is about 20363.7206816436. The cubic root of 414681120 is about 745.7124964568.

The spelling of 414681120 in words is "four hundred fourteen million, six hundred eighty-one thousand, one hundred twenty".