89312284800 has 360 divisors, whose sum is σ = 330144396285. Its totient is φ = 23776035840.

The previous prime is 89312284793. The next prime is 89312284807. The reversal of 89312284800 is 848221398.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is an interprime number because it is at equal distance from previous prime (89312284793) and next prime (89312284807).

It can be written as a sum of positive squares in 2 ways, for example, as 87526039104 + 1786245696 = 295848^2 + 42264^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=211320.

It is a super-2 number, since 2×89312284800² (a number of 23 digits) contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (89312284807) by changing a digit.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 152150107 + ... + 152150693.

Almost surely, 2^89312284800 is an apocalyptic number.

89312284800 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 89312284800

89312284800 is an abundant number, since it is smaller than the sum of its proper divisors (240832111485).

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

89312284800 is an frugal number, since it uses more digits than its factorization.

89312284800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1210 (or 597 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 45.

The spelling of 89312284800 in words is "eighty-nine billion, three hundred twelve million, two hundred eighty-four thousand, eight hundred".