416456820 has 432 divisors, whose sum is σ = 1572676560. Its totient is φ = 88252416.

The previous prime is 416456813. The next prime is 416456851. The reversal of 416456820 is 28654614.

416456820 is a `hidden beast` number, since 4 + 1 + 645 + 6 + 8 + 2 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 4691556 + 411765264 = 2166^2 + 20292^2 .

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 143 ways as a sum of consecutive naturals, for example, 14360566 + ... + 14360594.

It is an arithmetic number, because the mean of its divisors is an integer number (3640455).

Almost surely, 2^416456820 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 416456820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (786338280).

416456820 is an abundant number, since it is smaller than the sum of its proper divisors (1156219740).

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

416456820 is a wasteful number, since it uses less digits than its factorization.

416456820 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 112 (or 88 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The square root of 416456820 is about 20407.2737032657. The cubic root of 416456820 is about 746.7753823241.

The spelling of 416456820 in words is "four hundred sixteen million, four hundred fifty-six thousand, eight hundred twenty".