414728160 has 384 divisors, whose sum is σ = 1669248000. Its totient is φ = 85800960.

The previous prime is 414728131. The next prime is 414728173. The reversal of 414728160 is 61827414.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 1810926 + ... + 1811154.

It is an arithmetic number, because the mean of its divisors is an integer number (4347000).

Almost surely, 2^414728160 is an apocalyptic number.

414728160 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 414728160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (834624000).

414728160 is an abundant number, since it is smaller than the sum of its proper divisors (1254519840).

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

414728160 is a wasteful number, since it uses less digits than its factorization.

414728160 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 279 (or 257 counting only the distinct ones).

The product of its (nonzero) digits is 10752, while the sum is 33.

The square root of 414728160 is about 20364.8756441084. The cubic root of 414728160 is about 745.7406924110.

The spelling of 414728160 in words is "four hundred fourteen million, seven hundred twenty-eight thousand, one hundred sixty".