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85344 = 2537127
BaseRepresentation
bin10100110101100000
311100001220
4110311200
510212334
61455040
7503550
oct246540
9140056
1085344
1159136
1241480
132cacc
1423160
151a449
hex14d60

85344 has 48 divisors (see below), whose sum is σ = 258048. Its totient is φ = 24192.

The previous prime is 85333. The next prime is 85361. The reversal of 85344 is 44358.

85344 = 12 + 22 + ... + 632.

It is a happy number.

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 (24).

It is a d-powerful number, because it can be written as 85 + 53 + 39 + 47 + 47 .

It is a congruent number.

It is an unprimeable number.

85344 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 (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 609 + ... + 735.

It is an arithmetic number, because the mean of its divisors is an integer number (5376).

285344 is an apocalyptic number.

85344 is a gapful number since it is divisible by the number (84) 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 85344, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129024).

85344 is an abundant number, since it is smaller than the sum of its proper divisors (172704).

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

85344 is a wasteful number, since it uses less digits than its factorization.

85344 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 147 (or 139 counting only the distinct ones).

The product of its digits is 1920, while the sum is 24.

The square root of 85344 is about 292.1369541842. The cubic root of 85344 is about 44.0275309795.

The spelling of 85344 in words is "eighty-five thousand, three hundred forty-four".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 84 96 112 127 168 224 254 336 381 508 672 762 889 1016 1524 1778 2032 2667 3048 3556 4064 5334 6096 7112 10668 12192 14224 21336 28448 42672 85344