417661920 has 480 divisors, whose sum is σ = 1654617888. Its totient is φ = 98537472.

The previous prime is 417661877. The next prime is 417661931. The reversal of 417661920 is 29166714.

417661920 is a `hidden beast` number, since 4 + 17 + 6 + 619 + 20 = 666.

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 an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 6233727 + ... + 6233793.

Almost surely, 2^417661920 is an apocalyptic number.

417661920 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 417661920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (827308944).

417661920 is an abundant number, since it is smaller than the sum of its proper divisors (1236955968).

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

417661920 is a wasteful number, since it uses less digits than its factorization.

417661920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 144 (or 127 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 36.

The square root of 417661920 is about 20436.7786111217. The cubic root of 417661920 is about 747.4950026325.

The spelling of 417661920 in words is "four hundred seventeen million, six hundred sixty-one thousand, nine hundred twenty".