415717120 has 288 divisors, whose sum is σ = 1269176832. Its totient is φ = 126959616.

The previous prime is 415717091. The next prime is 415717123. The reversal of 415717120 is 21717514.

It is a super-2 number, since 2×415717120² = 345641447722188800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (28).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415717123) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 5008599 + ... + 5008681.

It is an arithmetic number, because the mean of its divisors is an integer number (4406864).

Almost surely, 2^415717120 is an apocalyptic number.

415717120 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 415717120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (634588416).

415717120 is an abundant number, since it is smaller than the sum of its proper divisors (853459712).

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

415717120 is a wasteful number, since it uses less digits than its factorization.

415717120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 167 (or 153 counting only the distinct ones).

The product of its (nonzero) digits is 1960, while the sum is 28.

The square root of 415717120 is about 20389.1422085383. The cubic root of 415717120 is about 746.3329858229.

The spelling of 415717120 in words is "four hundred fifteen million, seven hundred seventeen thousand, one hundred twenty".