416564640 has 192 divisors, whose sum is σ = 1468091520. Its totient is φ = 110315520.

The previous prime is 416564627. The next prime is 416564647. The reversal of 416564640 is 46465614.

416564640 is a `hidden beast` number, since 4 + 1 + 6 + 5 + 6 + 4 + 640 = 666.

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 = 416564595 and 416564604.

It is not an unprimeable number, because it can be changed into a prime (416564647) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 911292 + ... + 911748.

It is an arithmetic number, because the mean of its divisors is an integer number (7646310).

Almost surely, 2^416564640 is an apocalyptic number.

416564640 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 416564640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (734045760).

416564640 is an abundant number, since it is smaller than the sum of its proper divisors (1051526880).

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

416564640 is a wasteful number, since it uses less digits than its factorization.

416564640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 692 (or 678 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

The square root of 416564640 is about 20409.9152374526. The cubic root of 416564640 is about 746.8398230779.

The spelling of 416564640 in words is "four hundred sixteen million, five hundred sixty-four thousand, six hundred forty".