417415680 has 480 divisors, whose sum is σ = 1662268608. Its totient is φ = 99532800.

The previous prime is 417415657. The next prime is 417415681. The reversal of 417415680 is 86514714.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (417415681) 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, 6842850 + ... + 6842910.

Almost surely, 2^417415680 is an apocalyptic number.

417415680 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 417415680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (831134304).

417415680 is an abundant number, since it is smaller than the sum of its proper divisors (1244852928).

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

417415680 is an equidigital number, since it uses as much as digits as its factorization.

417415680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 110 (or 82 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 417415680 is about 20430.7532900772. The cubic root of 417415680 is about 747.3480741040.

The spelling of 417415680 in words is "four hundred seventeen million, four hundred fifteen thousand, six hundred eighty".