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34272 = 2532717
BaseRepresentation
bin1000010111100000
31202000100
420113200
52044042
6422400
7201630
oct102740
952010
1034272
1123827
1217a00
13127a4
14c6c0
15a24c
hex85e0

34272 has 72 divisors (see below), whose sum is σ = 117936. Its totient is φ = 9216.

The previous prime is 34267. The next prime is 34273. The reversal of 34272 is 27243.

It can be divided in two parts, 342 and 72, that added together give a palindrome (414).

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (72).

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 a d-powerful number, because it can be written as 36 + 44 + 29 + 7 + 215 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (34273) by changing a digit.

34272 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 11 ways as a sum of consecutive naturals, for example, 2008 + ... + 2024.

It is an arithmetic number, because the mean of its divisors is an integer number (1638).

234272 is an apocalyptic number.

34272 is a gapful number since it is divisible by the number (32) 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 34272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (58968).

34272 is an abundant number, since it is smaller than the sum of its proper divisors (83664).

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

34272 is a wasteful number, since it uses less digits than its factorization.

34272 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 40 (or 29 counting only the distinct ones).

The product of its digits is 336, while the sum is 18.

The square root of 34272 is about 185.1269834465. The cubic root of 34272 is about 32.4822783069.

The spelling of 34272 in words is "thirty-four thousand, two hundred seventy-two".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 17 18 21 24 28 32 34 36 42 48 51 56 63 68 72 84 96 102 112 119 126 136 144 153 168 204 224 238 252 272 288 306 336 357 408 476 504 544 612 672 714 816 952 1008 1071 1224 1428 1632 1904 2016 2142 2448 2856 3808 4284 4896 5712 8568 11424 17136 34272