36305204144400 has 405 divisors, whose sum is σ = 126826449130927. Its totient is φ = 9617470540800.

The previous prime is 36305204144387. The next prime is 36305204144449. The reversal of 36305204144400 is 444140250363.

The square root of 36305204144400 is 6025380.

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

36305204144400 is a `hidden beast` number, since 3 + 6 + 3 + 0 + 5 + 204 + 1 + 4 + 440 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 7149869557776 + 29155334586624 = 2673924^2 + 5399568^2 .

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

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 84234812185 + ... + 84234812615.

Almost surely, 2^{36305204144400} is an apocalyptic number.

36305204144400 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

36305204144400 is the 6025380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 36305204144400

36305204144400 is an abundant number, since it is smaller than the sum of its proper divisors (90521244986527).

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

36305204144400 is an equidigital number, since it uses as much as digits as its factorization.

36305204144400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1352 (or 674 counting only the distinct ones).

The product of its (nonzero) digits is 138240, while the sum is 36.

36305204144400 divided by its sum of digits (36) gives a square (1008477892900 = 1004230²).

Adding to 36305204144400 its reverse (444140250363), we get a palindrome (36749344394763).

The spelling of 36305204144400 in words is "thirty-six trillion, three hundred five billion, two hundred four million, one hundred forty-four thousand, four hundred".