414973440 has 480 divisors, whose sum is σ = 1715890176. Its totient is φ = 90685440.

The previous prime is 414973439. The next prime is 414973453. The reversal of 414973440 is 44379414.

414973440 is a `hidden beast` number, since 4 + 149 + 73 + 440 = 666.

It is a tau number, because it is divible by the number of its divisors (480).

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

It is a junction number, because it is equal to n+sod(n) for n = 414973395 and 414973404.

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, 4999639 + ... + 4999721.

Almost surely, 2^414973440 is an apocalyptic number.

414973440 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 414973440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (857945088).

414973440 is an abundant number, since it is smaller than the sum of its proper divisors (1300916736).

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

414973440 is a wasteful number, since it uses less digits than its factorization.

414973440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 150 (or 131 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 36.

The square root of 414973440 is about 20370.8968874716. The cubic root of 414973440 is about 745.8876796397.

The spelling of 414973440 in words is "four hundred fourteen million, nine hundred seventy-three thousand, four hundred forty".