• 164 can be written using four 4's:

164 has 6 divisors (see below), whose sum is σ = 294. Its totient is φ = 80.

The previous prime is 163. The next prime is 167. The reversal of 164 is 461.

Added to its reverse (461) it gives a 4-th power (625 = 5^{4}).

164 = T_{2} + T_{3} + ... +
T_{9}.

164 is nontrivially palindromic in base 3, base 7 and base 9.

164 is an esthetic number in base 6, base 7 and base 14, because in such bases its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 100 + 64 = 10^2 + 8^2 .

164 is an undulating number in base 7 and base 9.

It is a plaindrome in base 5, base 8, base 11, base 12 and base 15.

It is a nialpdrome in base 4, base 6, base 13, base 14 and base 16.

It is a congruent number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 17 + ... + 24.

It is an arithmetic number, because the mean of its divisors is an integer number (49).

It is an amenable number.

164 is a deficient number, since it is larger than the sum of its proper divisors (130).

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

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

The sum of its prime factors is 45 (or 43 counting only the distinct ones).

The product of its digits is 24, while the sum is 11.

The square root of 164 is about 12.8062484749. The cubic root of 164 is about 5.4737036748.

Subtracting from 164 its sum of digits (11), we obtain a triangular number (153 = T_{17}).

Adding to 164 its reverse (461), we get a 4-th power (625 = 5^{4}).

It can be divided in two parts, 16 and 4, that multiplied together give a 6-th power (64 = 2^{6}).

The spelling of 164 in words is "one hundred sixty-four", and thus it is an aban number.

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