417616560 has 300 divisors, whose sum is σ = 1547692608. Its totient is φ = 104343552.

The previous prime is 417616547. The next prime is 417616579. The reversal of 417616560 is 65616714.

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

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 1872609 + ... + 1872831.

Almost surely, 2^417616560 is an apocalyptic number.

417616560 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 417616560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (773846304).

417616560 is an abundant number, since it is smaller than the sum of its proper divisors (1130076048).

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

417616560 is a wasteful number, since it uses less digits than its factorization.

417616560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 282 (or 250 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The square root of 417616560 is about 20435.6688170463. The cubic root of 417616560 is about 747.4679411910.

It can be divided in two parts, 4176 and 16560, that added together give a 4-th power (20736 = 12⁴).

The spelling of 417616560 in words is "four hundred seventeen million, six hundred sixteen thousand, five hundred sixty".