8640 has 56 divisors (see below), whose sum is σ = 30480. Its totient is φ = 2304.

The previous prime is 8629. The next prime is 8641. The reversal of 8640 is 468.

It is a Jordan-Polya number, since it can be written as 6! ⋅ 3! ⋅ 2!.

8640 is an esthetic number in base 11 and base 14, because in such bases its adjacent digits differ by 1.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 10 and base 12.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (8641) by changing a digit.

8640 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 7 ways as a sum of consecutive naturals, for example, 1726 + ... + 1730.

2^{8640} is an apocalyptic number.

8640 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

8640 is the 54-th octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 8640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15240).

8640 is an abundant number, since it is smaller than the sum of its proper divisors (21840).

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

8640 is a wasteful number, since it uses less digits than its factorization.

8640 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 192, while the sum is 18.

The square root of 8640 is about 92.9516003090. The cubic root of 8640 is about 20.5197113601.

Subtracting from 8640 its product of nonzero digits (192), we obtain a palindrome (8448).

8640 divided by its product of nonzero digits (192) gives a triangular number (45 = T_{9}).

The spelling of 8640 in words is "eight thousand, six hundred forty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 64 72 80 90 96 108 120 135 144 160 180 192 216 240 270 288 320 360 432 480 540 576 720 864 960 1080 1440 1728 2160 2880 4320 8640

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