4500 has 36 divisors (see below), whose sum is σ = 14196. Its totient is φ = 1200.

The previous prime is 4493. The next prime is 4507. The reversal of 4500 is 54.

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 (4493) and next prime (4507).

It can be written as a sum of positive squares in 2 ways, for example, as 144 + 4356 = 12^2 + 66^2 .

It is a tau number, because it is divible by the number of its divisors (36).

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 congruent number.

It is not an unprimeable number, because it can be changed into a prime (4507) by changing a digit.

4500 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 898 + ... + 902.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4500, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7098).

4500 is an abundant number, since it is smaller than the sum of its proper divisors (9696).

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

4500 is a wasteful number, since it uses less digits than its factorization.

4500 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 25 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 4500 is about 67.0820393250. The cubic root of 4500 is about 16.5096362445.

Multiplying 4500 by its product of nonzero digits (20), we get a square (90000 = 300^{2}).

4500 divided by its product of nonzero digits (20) gives a square (225 = 15^{2}).

Adding to 4500 its reverse (54), we get a palindrome (4554).

The spelling of 4500 in words is "four thousand, five hundred".

Divisors: 1 2 3 4 5 6 9 10 12 15 18 20 25 30 36 45 50 60 75 90 100 125 150 180 225 250 300 375 450 500 750 900 1125 1500 2250 4500

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