69984 has 48 divisors (see below), whose sum is σ = 206640. Its totient is φ = 23328.

The previous prime is 69959. The next prime is 69991. The reversal of 69984 is 48996.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (36).

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

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 69984.

It is an unprimeable number.

69984 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 7 ways as a sum of consecutive naturals, for example, 23327 + 23328 + 23329.

It is an arithmetic number, because the mean of its divisors is an integer number (4305).

69984 is a Friedman number, since it can be written as 9*6^(9-8+4), using all its digits and the basic arithmetic operations.

2^{69984} 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 69984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (103320).

69984 is an abundant number, since it is smaller than the sum of its proper divisors (136656).

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

69984 is an frugal number, since it uses more digits than its factorization.

69984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 31 (or 5 counting only the distinct ones).

The product of its digits is 15552, while the sum is 36.

The square root of 69984 is about 264.5448922206. The cubic root of 69984 is about 41.2097127319.

It can be divided in two parts, 69 and 984, that multiplied together give a triangular number (67896 = T_{368}).

The spelling of 69984 in words is "sixty-nine thousand, nine hundred eighty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 72 81 96 108 144 162 216 243 288 324 432 486 648 729 864 972 1296 1458 1944 2187 2592 2916 3888 4374 5832 7776 8748 11664 17496 23328 34992 69984

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