217728 has 96 divisors (see below), whose sum is σ = 742560. Its totient is φ = 62208.

The previous prime is 217727. The next prime is 217733. The reversal of 217728 is 827712.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

It is a nialpdrome in base 6 and base 12.

It is a zygodrome in base 6.

It is not an unprimeable number, because it can be changed into a prime (217727) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 31101 + ... + 31107.

It is an arithmetic number, because the mean of its divisors is an integer number (7735).

217728 is a Friedman number, since it can be written as (12^(7-2)*7)/8, using all its digits and the basic arithmetic operations.

2^{217728} is an apocalyptic number.

217728 is a gapful number since it is divisible by the number (28) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 217728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (371280).

217728 is an abundant number, since it is smaller than the sum of its proper divisors (524832).

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

217728 is an frugal number, since it uses more digits than its factorization.

217728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 12 counting only the distinct ones).

The product of its digits is 1568, while the sum is 27.

The square root of 217728 is about 466.6133302854. The cubic root of 217728 is about 60.1595752196.

The spelling of 217728 in words is "two hundred seventeen thousand, seven hundred twenty-eight".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 64 72 81 84 96 108 112 126 128 144 162 168 189 192 216 224 243 252 288 324 336 378 384 432 448 486 504 567 576 648 672 756 864 896 972 1008 1134 1152 1296 1344 1512 1701 1728 1944 2016 2268 2592 2688 3024 3402 3456 3888 4032 4536 5184 6048 6804 7776 8064 9072 10368 12096 13608 15552 18144 24192 27216 31104 36288 54432 72576 108864 217728

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