27720 has 96 divisors (see below), whose sum is σ = 112320. Its totient is φ = 5760.

The previous prime is 27701. The next prime is 27733. The reversal of 27720 is 2772.

27720 = T_{1} + T_{2} + ... +
T_{54}.

27720 is a nontrivial binomial coefficient, being equal to C(56, 3).

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

It is a nialpdrome in base 6, base 8 and base 15.

It is a zygodrome in base 6.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 27693 and 27702.

It is an unprimeable number.

27720 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is the 54-th tetrahedral number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2515 + ... + 2525.

It is an arithmetic number, because the mean of its divisors is an integer number (1170).

27720 is a highly composite number, because it has more divisors than any smaller number.

27720 is a superabundant number, because it has a larger abundancy index than any smaller number.

2^{27720} is an apocalyptic number.

27720 is a gapful number since it is divisible by the number (20) 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 27720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (56160).

27720 is an abundant number, since it is smaller than the sum of its proper divisors (84600).

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

27720 is a wasteful number, since it uses less digits than its factorization.

27720 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 196, while the sum is 18.

The square root of 27720 is about 166.4932431061. The cubic root of 27720 is about 30.2643308006.

27720 divided by its sum of digits (18) gives a triangular number (1540 = T_{55}).

It can be divided in two parts, 27 and 720, that added together give a palindrome (747).

The spelling of 27720 in words is "twenty-seven thousand, seven hundred twenty", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 18 20 21 22 24 28 30 33 35 36 40 42 44 45 55 56 60 63 66 70 72 77 84 88 90 99 105 110 120 126 132 140 154 165 168 180 198 210 220 231 252 264 280 308 315 330 360 385 396 420 440 462 495 504 616 630 660 693 770 792 840 924 990 1155 1260 1320 1386 1540 1848 1980 2310 2520 2772 3080 3465 3960 4620 5544 6930 9240 13860 27720

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