121584 has 40 divisors (see below), whose sum is σ = 334800. Its totient is φ = 37888.

The previous prime is 121579. The next prime is 121591. The reversal of 121584 is 485121.

121584 = T₆₇ + T₆₈ + ... + T₁₀₀.

It is a self number, because there is not a number n which added to its sum of digits gives 121584.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 121584.

It is an unprimeable number.

121584 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 7 ways as a sum of consecutive naturals, for example, 742 + ... + 890.

It is an arithmetic number, because the mean of its divisors is an integer number (8370).

2¹²¹⁵⁸⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 121584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (167400).

121584 is an abundant number, since it is smaller than the sum of its proper divisors (213216).

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

121584 is a wasteful number, since it uses less digits than its factorization.

121584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 177 (or 171 counting only the distinct ones).

The product of its digits is 320, while the sum is 21.

The square root of 121584 is about 348.6889731552. The cubic root of 121584 is about 49.5403201735.

It can be divided in two parts, 12 and 1584, that added together give a triangular number (1596 = T₅₆).

The spelling of 121584 in words is "one hundred twenty-one thousand, five hundred eighty-four".