7705328400 has 1215 divisors, whose sum is σ = 36084293973. Its totient is φ = 1516838400.

The previous prime is 7705328383. The next prime is 7705328429. The reversal of 7705328400 is 48235077.

The square root of 7705328400 is 87780.

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

It can be written as a sum of positive squares in only one way, i.e., 2773918224 + 4931410176 = 52668^2 + 70224^2 .

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 (17) of ones.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 405543591 + ... + 405543609.

Almost surely, 2^7705328400 is an apocalyptic number.

7705328400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

7705328400 is the 87780-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7705328400

7705328400 is an abundant number, since it is smaller than the sum of its proper divisors (28378965573).

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

7705328400 is a wasteful number, since it uses less digits than its factorization.

7705328400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 47040, while the sum is 36.

The cubic root of 7705328400 is about 1975.1362102287.

Multiplying 7705328400 by its sum of digits (36), we get a square (277391822400 = 526680²).

7705328400 divided by its sum of digits (36) gives a square (214036900 = 14630²).

The spelling of 7705328400 in words is "seven billion, seven hundred five million, three hundred twenty-eight thousand, four hundred".