90089949600 has 1080 divisors, whose sum is σ = 404903420460. Its totient is φ = 19369082880.

The previous prime is 90089949581. The next prime is 90089949619. The reversal of 90089949600 is 694998009.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (90089949581) and next prime (90089949619).

It can be written as a sum of positive squares in 6 ways, for example, as 47076848784 + 43013100816 = 216972^2 + 207396^2 .

It is a tau number, because it is divible by the number of its divisors (1080).

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

It is an unprimeable number.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 53977566 + ... + 53979234.

Almost surely, 2^90089949600 is an apocalyptic number.

90089949600 is a gapful number since it is divisible by the number (90) 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 90089949600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202451710230).

90089949600 is an abundant number, since it is smaller than the sum of its proper divisors (314813470860).

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

90089949600 is a wasteful number, since it uses less digits than its factorization.

90089949600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1732 (or 1703 counting only the distinct ones).

The product of its (nonzero) digits is 1259712, while the sum is 54.

The spelling of 90089949600 in words is "ninety billion, eighty-nine million, nine hundred forty-nine thousand, six hundred".