90000 has 75 divisors (see below), whose sum is σ = 314743. Its totient is φ = 24000.

The previous prime is 89989. The next prime is 90001. The reversal of 90000 is 9.

90000 = T_{299} + T_{300}.

90000 = 1^{3} + 2^{3} + ... + 24^{3}.

The square root of 90000 is 300.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 2 ways, for example, as 7056 + 82944 = 84^2 + 288^2 .

It is a tau number, because it is divible by the number of its divisors (75).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a Duffinian number.

It is a nialpdrome in base 10 and base 12.

It is not an unprimeable number, because it can be changed into a prime (90001) by changing a digit.

90000 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 14 ways as a sum of consecutive naturals, for example, 17998 + ... + 18002.

2^{90000} is an apocalyptic number.

90000 is a gapful number since it is divisible by the number (90) formed by its first and last digit.

90000 is the 300-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 90000

90000 is an abundant number, since it is smaller than the sum of its proper divisors (224743).

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

90000 is a wasteful number, since it uses less digits than its factorization.

90000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 34 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 9, while the sum is 9.

The cubic root of 90000 is about 44.8140474656.

The spelling of 90000 in words is "ninety thousand".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 40 45 48 50 60 72 75 80 90 100 120 125 144 150 180 200 225 240 250 300 360 375 400 450 500 600 625 720 750 900 1000 1125 1200 1250 1500 1800 1875 2000 2250 2500 3000 3600 3750 4500 5000 5625 6000 7500 9000 10000 11250 15000 18000 22500 30000 45000 90000

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