417947040 has 480 divisors, whose sum is σ = 1791465984. Its totient is φ = 89579520.

The previous prime is 417947003. The next prime is 417947041. The reversal of 417947040 is 40749714.

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 junction number, because it is equal to n+sod(n) for n = 417946986 and 417947004.

It is not an unprimeable number, because it can be changed into a prime (417947041) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 1542105 + ... + 1542375.

Almost surely, 2^417947040 is an apocalyptic number.

417947040 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 417947040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (895732992).

417947040 is an abundant number, since it is smaller than the sum of its proper divisors (1373518944).

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

417947040 is a wasteful number, since it uses less digits than its factorization.

417947040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 322 (or 305 counting only the distinct ones).

The product of its (nonzero) digits is 28224, while the sum is 36.

The square root of 417947040 is about 20443.7530800976. The cubic root of 417947040 is about 747.6650582732.

The spelling of 417947040 in words is "four hundred seventeen million, nine hundred forty-seven thousand, forty".