87825628800 has 2304 divisors, whose sum is σ = 424292843520. Its totient is φ = 16787865600.

The previous prime is 87825628799. The next prime is 87825628801. The reversal of 87825628800 is 882652878.

87825628800 is a `hidden beast` number, since 8 + 7 + 8 + 2 + 5 + 628 + 8 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (87825628799) and next prime (87825628801).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (87825628801) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1868630377 + ... + 1868630423.

It is an arithmetic number, because the mean of its divisors is an integer number (184154880).

Almost surely, 2^87825628800 is an apocalyptic number.

87825628800 is a gapful number since it is divisible by the number (80) 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 87825628800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (212146421760).

87825628800 is an abundant number, since it is smaller than the sum of its proper divisors (336467214720).

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

87825628800 is a wasteful number, since it uses less digits than its factorization.

87825628800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 151 (or 131 counting only the distinct ones).

The product of its (nonzero) digits is 3440640, while the sum is 54.

The spelling of 87825628800 in words is "eighty-seven billion, eight hundred twenty-five million, six hundred twenty-eight thousand, eight hundred".