417749472 has 288 divisors, whose sum is σ = 1429908480. Its totient is φ = 113218560.

The previous prime is 417749461. The next prime is 417749477. The reversal of 417749472 is 274947714.

417749472 is a `hidden beast` number, since 4 + 177 + 4 + 9 + 472 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (417749477) 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, 5287929 + ... + 5288007.

It is an arithmetic number, because the mean of its divisors is an integer number (4964960).

Almost surely, 2^417749472 is an apocalyptic number.

417749472 is a gapful number since it is divisible by the number (42) 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 417749472, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (714954240).

417749472 is an abundant number, since it is smaller than the sum of its proper divisors (1012159008).

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

417749472 is a wasteful number, since it uses less digits than its factorization.

417749472 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 206 (or 195 counting only the distinct ones).

The product of its digits is 395136, while the sum is 45.

The square root of 417749472 is about 20438.9205194404. The cubic root of 417749472 is about 747.5472299699.

The spelling of 417749472 in words is "four hundred seventeen million, seven hundred forty-nine thousand, four hundred seventy-two".