413397561600 has 1215 divisors, whose sum is σ = 1648255368837. Its totient is φ = 102215208960.

The previous prime is 413397561593. The next prime is 413397561607. The reversal of 413397561600 is 6165793314.

It is a happy number.

The square root of 413397561600 is 642960.

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

413397561600 is a `hidden beast` number, since 4 + 1 + 3 + 39 + 7 + 5 + 6 + 1 + 600 = 666.

It is an interprime number because it is at equal distance from previous prime (413397561593) and next prime (413397561607).

It can be written as a sum of positive squares in only one way, i.e., 148823122176 + 264574439424 = 385776^2 + 514368^2 .

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

It is not an unprimeable number, because it can be changed into a prime (413397561607) by changing a digit.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 8795692777 + ... + 8795692823.

Almost surely, 2^413397561600 is an apocalyptic number.

413397561600 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

413397561600 is the 642960-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413397561600

413397561600 is an abundant number, since it is smaller than the sum of its proper divisors (1234857807237).

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

413397561600 is an equidigital number, since it uses as much as digits as its factorization.

413397561600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 170 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 408240, while the sum is 45.

The spelling of 413397561600 in words is "four hundred thirteen billion, three hundred ninety-seven million, five hundred sixty-one thousand, six hundred".