87638284800 has 480 divisors, whose sum is σ = 350933520960. Its totient is φ = 21244723200.

The previous prime is 87638284787. The next prime is 87638284801. The reversal of 87638284800 is 848283678.

87638284800 is a `hidden beast` number, since 87 + 6 + 3 + 82 + 8 + 480 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (480).

It is a super-2 number, since 2×87638284800² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (87638284801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3790074 + ... + 3813126.

It is an arithmetic number, because the mean of its divisors is an integer number (731111502).

Almost surely, 2^87638284800 is an apocalyptic number.

87638284800 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 87638284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175466760480).

87638284800 is an abundant number, since it is smaller than the sum of its proper divisors (263295236160).

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

87638284800 is a wasteful number, since it uses less digits than its factorization.

87638284800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23101 (or 23074 counting only the distinct ones).

The product of its (nonzero) digits is 4128768, while the sum is 54.

The spelling of 87638284800 in words is "eighty-seven billion, six hundred thirty-eight million, two hundred eighty-four thousand, eight hundred".