61577625600 has 630 divisors, whose sum is σ = 235992402030. Its totient is φ = 15854469120.

The previous prime is 61577625583. The next prime is 61577625611. The reversal of 61577625600 is 652677516.

61577625600 is a `hidden beast` number, since 6 + 15 + 7 + 7 + 6 + 25 + 600 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 4161798144 + 57415827456 = 64512^2 + 239616^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 2123366386 + ... + 2123366414.

Almost surely, 2^61577625600 is an apocalyptic number.

61577625600 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 61577625600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (117996201015).

61577625600 is an abundant number, since it is smaller than the sum of its proper divisors (174414776430).

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

61577625600 is an frugal number, since it uses more digits than its factorization.

61577625600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 91 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 529200, while the sum is 45.

The spelling of 61577625600 in words is "sixty-one billion, five hundred seventy-seven million, six hundred twenty-five thousand, six hundred".