821760380100 has 729 divisors, whose sum is σ = 2945907005223. Its totient is φ = 191454912000.

The previous prime is 821760380017. The next prime is 821760380107. The reversal of 821760380100 is 1083067128.

The square root of 821760380100 is 906510.

It is a perfect power (a square), and thus also a powerful number.

821760380100 is a `hidden beast` number, since 8 + 2 + 176 + 0 + 380 + 100 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 345892191876 + 475868188224 = 588126^2 + 689832^2 .

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

It is not an unprimeable number, because it can be changed into a prime (821760380107) by changing a digit.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 12265080267 + ... + 12265080333.

Almost surely, 2^821760380100 is an apocalyptic number.

821760380100 is the 906510-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 821760380100

821760380100 is an abundant number, since it is smaller than the sum of its proper divisors (2124146625123).

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

821760380100 is a wasteful number, since it uses less digits than its factorization.

821760380100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 258 (or 129 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

Multiplying 821760380100 by its sum of digits (36), we get a square (29583373683600 = 5439060²).

821760380100 divided by its sum of digits (36) gives a square (22826677225 = 151085²).

The spelling of 821760380100 in words is "eight hundred twenty-one billion, seven hundred sixty million, three hundred eighty thousand, one hundred".