414516480 has 216 divisors, whose sum is σ = 1540701792. Its totient is φ = 94703616.

The previous prime is 414516461. The next prime is 414516481. The reversal of 414516480 is 84615414.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414516481) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 187059 + ... + 189261.

Almost surely, 2^414516480 is an apocalyptic number.

414516480 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 414516480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (770350896).

414516480 is an abundant number, since it is smaller than the sum of its proper divisors (1126185312).

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

414516480 is a wasteful number, since it uses less digits than its factorization.

414516480 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2241 (or 2220 counting only the distinct ones).

The product of its (nonzero) digits is 15360, while the sum is 33.

The square root of 414516480 is about 20359.6777970576. The cubic root of 414516480 is about 745.6137938222.

The spelling of 414516480 in words is "four hundred fourteen million, five hundred sixteen thousand, four hundred eighty".