414996480 has 384 divisors, whose sum is σ = 1572480000. Its totient is φ = 103514112.

The previous prime is 414996479. The next prime is 414996497. The reversal of 414996480 is 84699414.

414996480 is a `hidden beast` number, since 41 + 49 + 96 + 480 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 5253081 + ... + 5253159.

It is an arithmetic number, because the mean of its divisors is an integer number (4095000).

Almost surely, 2^414996480 is an apocalyptic number.

414996480 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 414996480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (786240000).

414996480 is an abundant number, since it is smaller than the sum of its proper divisors (1157483520).

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

414996480 is a wasteful number, since it uses less digits than its factorization.

414996480 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 134 (or 108 counting only the distinct ones).

The product of its (nonzero) digits is 248832, while the sum is 45.

The square root of 414996480 is about 20371.4623922781. The cubic root of 414996480 is about 745.9014836831.

The spelling of 414996480 in words is "four hundred fourteen million, nine hundred ninety-six thousand, four hundred eighty".