415800 has 192 divisors, whose sum is σ = 1785600. Its totient is φ = 86400.

The previous prime is 415799. The next prime is 415801. The reversal of 415800 is 8514.

It is an interprime number because it is at equal distance from previous prime (415799) and next prime (415801).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 15.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 37795 + ... + 37805.

It is an arithmetic number, because the mean of its divisors is an integer number (9300).

2⁴¹⁵⁸⁰⁰ is an apocalyptic number.

415800 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 415800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (892800).

415800 is an abundant number, since it is smaller than the sum of its proper divisors (1369800).

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

415800 is a wasteful number, since it uses less digits than its factorization.

415800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 43 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 415800 is about 644.8255578061. The cubic root of 415800 is about 74.6382580419.

The spelling of 415800 in words is "four hundred fifteen thousand, eight hundred".