164640 has 96 divisors (see below), whose sum is σ = 604800. Its totient is φ = 37632.

The previous prime is 164627. The next prime is 164653. The reversal of 164640 is 46461.

It is an interprime number because it is at equal distance from previous prime (164627) and next prime (164653).

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 (21).

It is a nialpdrome in base 14.

It is a zygodrome in base 14.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 70 × 42 × 56.

It is a congruent number.

It is an unprimeable number.

164640 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 23517 + ... + 23523.

It is an arithmetic number, because the mean of its divisors is an integer number (6300).

2^{164640} is an apocalyptic number.

164640 is a gapful number since it is divisible by the number (10) 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 164640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (302400).

164640 is an abundant number, since it is smaller than the sum of its proper divisors (440160).

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

164640 is an equidigital number, since it uses as much as digits as its factorization.

164640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 164640 is about 405.7585488933. The cubic root of 164640 is about 54.8081469764.

It can be divided in two parts, 16 and 4640, that added together give a triangular number (4656 = T_{96}).

The spelling of 164640 in words is "one hundred sixty-four thousand, six hundred forty".

Divisors: 1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 28 30 32 35 40 42 48 49 56 60 70 80 84 96 98 105 112 120 140 147 160 168 196 210 224 240 245 280 294 336 343 392 420 480 490 560 588 672 686 735 784 840 980 1029 1120 1176 1372 1470 1568 1680 1715 1960 2058 2352 2744 2940 3360 3430 3920 4116 4704 5145 5488 5880 6860 7840 8232 10290 10976 11760 13720 16464 20580 23520 27440 32928 41160 54880 82320 164640

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