8100 has 45 divisors (see below), whose sum is σ = 26257. Its totient is φ = 2160.

The previous prime is 8093. The next prime is 8101. The reversal of 8100 is 18.

8100 = T_{89} + T_{90}.

The square root of 8100 is 90.

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

It can be written as a sum of positive squares in only one way, i.e., 2916 + 5184 = 54^2 + 72^2 .

It is a tau number, because it is divible by the number of its divisors (45).

It is a super-2 number, since 2×8100^{2} = 131220000, which contains 22 as substring.

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

It is a Duffinian number.

It is a nialpdrome in base 10.

It is a zygodrome in base 5.

It is not an unprimeable number, because it can be changed into a prime (8101) by changing a digit.

8100 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, 1618 + ... + 1622.

2^{8100} is an apocalyptic number.

8100 is the 90-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 8100

8100 is an abundant number, since it is smaller than the sum of its proper divisors (18157).

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

8100 is a wasteful number, since it uses less digits than its factorization.

8100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 26 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 9.

The cubic root of 8100 is about 20.0829885025.

Adding to 8100 its reverse (18), we get a palindrome (8118).

The spelling of 8100 in words is "eight thousand, one hundred".

Divisors: 1 2 3 4 5 6 9 10 12 15 18 20 25 27 30 36 45 50 54 60 75 81 90 100 108 135 150 162 180 225 270 300 324 405 450 540 675 810 900 1350 1620 2025 2700 4050 8100

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