10406817921600 has 1323 divisors, whose sum is σ = 40152707643243. Its totient is φ = 2653442426880.

The previous prime is 10406817921587. The next prime is 10406817921611. The reversal of 10406817921600 is 612971860401.

The square root of 10406817921600 is 3225960.

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

10406817921600 is a `hidden beast` number, since 1 + 0 + 4 + 0 + 6 + 8 + 17 + 9 + 21 + 600 = 666.

10406817921600 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 4 ways, for example, as 143047342656 + 10263770578944 = 378216^2 + 3203712^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 188 ways as a sum of consecutive naturals, for example, 101037067149 + ... + 101037067251.

Almost surely, 2^{10406817921600} is an apocalyptic number.

10406817921600 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10406817921600 is the 3225960-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10406817921600

10406817921600 is an abundant number, since it is smaller than the sum of its proper divisors (29745889721643).

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

10406817921600 is an frugal number, since it uses more digits than its factorization.

10406817921600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 304 (or 142 counting only the distinct ones).

The product of its (nonzero) digits is 145152, while the sum is 45.

The spelling of 10406817921600 in words is "ten trillion, four hundred six billion, eight hundred seventeen million, nine hundred twenty-one thousand, six hundred".