75564512100 has 1215 divisors, whose sum is σ = 322631087051. Its totient is φ = 14778086400.

The previous prime is 75564512081. The next prime is 75564512167. The reversal of 75564512100 is 121546557.

The square root of 75564512100 is 274890.

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

75564512100 is a `hidden beast` number, since 7 + 5 + 5 + 645 + 1 + 2 + 1 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 1767529764 + 73796982336 = 42042^2 + 271656^2 .

It is a super-2 number, since 2×75564512100² (a number of 23 digits) contains 22 as substring.

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 (23) of ones.

It is a polite number, since it can be written in 404 ways as a sum of consecutive naturals, for example, 4444971292 + ... + 4444971308.

Almost surely, 2^75564512100 is an apocalyptic number.

75564512100 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

75564512100 is the 274890-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75564512100

75564512100 is an abundant number, since it is smaller than the sum of its proper divisors (247066574951).

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

75564512100 is a wasteful number, since it uses less digits than its factorization.

75564512100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 104 (or 45 counting only the distinct ones).

The product of its (nonzero) digits is 42000, while the sum is 36.

Multiplying 75564512100 by its sum of digits (36), we get a square (2720322435600 = 1649340²).

75564512100 divided by its sum of digits (36) gives a square (2099014225 = 45815²).

The spelling of 75564512100 in words is "seventy-five billion, five hundred sixty-four million, five hundred twelve thousand, one hundred".