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180144 = 2434139
BaseRepresentation
bin101011111110110000
3100011010000
4223332300
521231034
63510000
71350126
oct537660
9304100
10180144
11113388
1288300
1363cc3
1449916
1538599
hex2bfb0

180144 has 50 divisors (see below), whose sum is σ = 525140. Its totient is φ = 59616.

The previous prime is 180137. The next prime is 180161. The reversal of 180144 is 441081.

It can be divided in two parts, 180 and 144, that added together give a square (324 = 182).

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

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

It is a plaindrome in base 11.

It is a nialpdrome in base 12.

It is a zygodrome in base 11.

It is an unprimeable number.

180144 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 (11) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 1227 + ... + 1365.

2180144 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 180144, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (262570).

180144 is an abundant number, since it is smaller than the sum of its proper divisors (344996).

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

180144 is a wasteful number, since it uses less digits than its factorization.

180144 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 159 (or 144 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 18.

The square root of 180144 is about 424.4337404119. The cubic root of 180144 is about 56.4772142960.

The spelling of 180144 in words is "one hundred eighty thousand, one hundred forty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72 81 108 139 144 162 216 278 324 417 432 556 648 834 1112 1251 1296 1668 2224 2502 3336 3753 5004 6672 7506 10008 11259 15012 20016 22518 30024 45036 60048 90072 180144