9072 has 50 divisors (see below), whose sum is σ = 30008. Its totient is φ = 2592.

The previous prime is 9067. The next prime is 9091. The reversal of 9072 is 2709.

Added to its reverse (2709) it gives a triangular number (11781 = T_{153}).

9072 is nontrivially palindromic in base 5.

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

It is an alternating number because its digits alternate between odd and even.

It is a nialpdrome in base 6 and base 12.

It is a zygodrome in base 6.

It is a congruent number.

It is an unprimeable number.

9072 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 9 ways as a sum of consecutive naturals, for example, 1293 + ... + 1299.

9072 is the 48-th decagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 9072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15004).

9072 is an abundant number, since it is smaller than the sum of its proper divisors (20936).

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

9072 is a wasteful number, since it uses less digits than its factorization.

9072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 27 (or 12 counting only the distinct ones).

The product of its (nonzero) digits is 126, while the sum is 18.

The square root of 9072 is about 95.2470471983. The cubic root of 9072 is about 20.8561598693.

Adding to 9072 its reverse (2709), we get a triangular number (11781 = T_{153}).

It can be divided in two parts, 907 and 2, that added together give a palindrome (909).

The spelling of 9072 in words is "nine thousand, seventy-two".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 36 42 48 54 56 63 72 81 84 108 112 126 144 162 168 189 216 252 324 336 378 432 504 567 648 756 1008 1134 1296 1512 2268 3024 4536 9072

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