417672000 has 168 divisors, whose sum is σ = 1494339912. Its totient is φ = 111360000.

The previous prime is 417671987. The next prime is 417672011. The reversal of 417672000 is 276714.

It can be written as a sum of positive squares in 4 ways, for example, as 5419584 + 412252416 = 2328^2 + 20304^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 69100 + ... + 74900.

Almost surely, 2^417672000 is an apocalyptic number.

417672000 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 417672000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (747169956).

417672000 is an abundant number, since it is smaller than the sum of its proper divisors (1076667912).

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

417672000 is a wasteful number, since it uses less digits than its factorization.

417672000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5834 (or 5811 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 417672000 is about 20437.0252238431. The cubic root of 417672000 is about 747.5010160201.

It can be divided in two parts, 4176 and 72000, that added together give a square (76176 = 276²).

The spelling of 417672000 in words is "four hundred seventeen million, six hundred seventy-two thousand".