661164134400 has 1755 divisors, whose sum is σ = 3030243699405. Its totient is φ = 137384755200.

The previous prime is 661164134383. The next prime is 661164134497. The reversal of 661164134400 is 4431461166.

The square root of 661164134400 is 813120.

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

661164134400 is a `hidden beast` number, since 6 + 6 + 1 + 1 + 641 + 3 + 4 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 238019088384 + 423145046016 = 487872^2 + 650496^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 60105830395 + ... + 60105830405.

Almost surely, 2^661164134400 is an apocalyptic number.

661164134400 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

661164134400 is the 813120-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 661164134400

661164134400 is an abundant number, since it is smaller than the sum of its proper divisors (2369079565005).

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

661164134400 is an equidigital number, since it uses as much as digits as its factorization.

661164134400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 36.

Multiplying 661164134400 by its sum of digits (36), we get a square (23801908838400 = 4878720²).

661164134400 divided by its sum of digits (36) gives a square (18365670400 = 135520²).

Adding to 661164134400 its reverse (4431461166), we get a palindrome (665595595566).

The spelling of 661164134400 in words is "six hundred sixty-one billion, one hundred sixty-four million, one hundred thirty-four thousand, four hundred".