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83232 = 2532172
BaseRepresentation
bin10100010100100000
311020011200
4110110200
510130412
61441200
7464442
oct242440
9136150
1083232
1157596
1240200
132bb66
1422492
15199dc
hex14520

83232 has 54 divisors (see below), whose sum is σ = 251433. Its totient is φ = 26112.

The previous prime is 83231. The next prime is 83233. The reversal of 83232 is 23238.

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 an interprime number because it is at equal distance from previous prime (83231) and next prime (83233).

It can be written as a sum of positive squares in 2 ways, for example, as 76176 + 7056 = 276^2 + 84^2 .

It is an ABA number since it can be written as A⋅BA, here for A=2, B=204.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is an alternating number because its digits alternate between even and odd.

It is not an unprimeable number, because it can be changed into a prime (83231) by changing a digit.

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 8 ways as a sum of consecutive naturals, for example, 4888 + ... + 4904.

283232 is an apocalyptic number.

It is a pronic number, being equal to 288×289.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 83232

83232 is an abundant number, since it is smaller than the sum of its proper divisors (168201).

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

83232 is a wasteful number, since it uses less digits than its factorization.

83232 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 50 (or 22 counting only the distinct ones).

The product of its digits is 288, while the sum is 18.

The square root of 83232 is about 288.4995667241. The cubic root of 83232 is about 43.6613114916.

Multiplying 83232 by its sum of digits (18), we get a square (1498176 = 12242).

83232 divided by its sum of digits (18) gives a square (4624 = 682).

Subtracting from 83232 its product of digits (288), we obtain a square (82944 = 2882).

Multiplying 83232 by its product of digits (288), we get a square (23970816 = 48962).

83232 divided by its product of digits (288) gives a square (289 = 172).

It can be divided in two parts, 8 and 3232, that added together give a triangular number (3240 = T80).

The spelling of 83232 in words is "eighty-three thousand, two hundred thirty-two".

Divisors: 1 2 3 4 6 8 9 12 16 17 18 24 32 34 36 48 51 68 72 96 102 136 144 153 204 272 288 289 306 408 544 578 612 816 867 1156 1224 1632 1734 2312 2448 2601 3468 4624 4896 5202 6936 9248 10404 13872 20808 27744 41616 83232