416723972688 has 480 divisors, whose sum is σ = 1291597332480. Its totient is φ = 124904263680.

The previous prime is 416723972659. The next prime is 416723972713. The reversal of 416723972688 is 886279327614.

416723972688 is a `hidden beast` number, since 4 + 167 + 2 + 397 + 2 + 6 + 88 = 666.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1135487481 + ... + 1135487847.

It is an arithmetic number, because the mean of its divisors is an integer number (2690827776).

Almost surely, 2^416723972688 is an apocalyptic number.

416723972688 is a gapful number since it is divisible by the number (48) 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 416723972688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (645798666240).

416723972688 is an abundant number, since it is smaller than the sum of its proper divisors (874873359792).

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

416723972688 is a wasteful number, since it uses less digits than its factorization.

416723972688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 655 (or 646 counting only the distinct ones).

The product of its digits is 48771072, while the sum is 63.

The spelling of 416723972688 in words is "four hundred sixteen billion, seven hundred twenty-three million, nine hundred seventy-two thousand, six hundred eighty-eight".