415680 has 56 divisors (see below), whose sum is σ = 1322832. Its totient is φ = 110592.

The previous prime is 415673. The next prime is 415687. The reversal of 415680 is 86514.

It is an interprime number because it is at equal distance from previous prime (415673) and next prime (415687).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an Ulam number.

It is a self number, because there is not a number n which added to its sum of digits gives 415680.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415687) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 744 + ... + 1176.

It is an arithmetic number, because the mean of its divisors is an integer number (23622).

2⁴¹⁵⁶⁸⁰ is an apocalyptic number.

415680 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 415680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (661416).

415680 is an abundant number, since it is smaller than the sum of its proper divisors (907152).

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

415680 is a wasteful number, since it uses less digits than its factorization.

415680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 453 (or 443 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 24.

The square root of 415680 is about 644.7325026707. The cubic root of 415680 is about 74.6310771434.

The spelling of 415680 in words is "four hundred fifteen thousand, six hundred eighty".