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180072 = 23324161
BaseRepresentation
bin101011111101101000
3100011000100
4223331220
521230242
63505400
71346664
oct537550
9304010
10180072
11113322
1288260
1363c69
14498a4
153854c
hex2bf68

180072 has 48 divisors (see below), whose sum is σ = 507780. Its totient is φ = 57600.

The previous prime is 180071. The next prime is 180073. The reversal of 180072 is 270081.

It is an interprime number because it is at equal distance from previous prime (180071) and next prime (180073).

It can be written as a sum of positive squares in 2 ways, for example, as 125316 + 54756 = 354^2 + 234^2 .

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

It is a zygodrome in base 11.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (180071) by changing a digit.

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 11 ways as a sum of consecutive naturals, for example, 2922 + ... + 2982.

2180072 is an apocalyptic number.

180072 is a gapful number since it is divisible by the number (12) 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 180072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (253890).

180072 is an abundant number, since it is smaller than the sum of its proper divisors (327708).

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

180072 is a wasteful number, since it uses less digits than its factorization.

180072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 114 (or 107 counting only the distinct ones).

The product of its (nonzero) digits is 112, while the sum is 18.

The square root of 180072 is about 424.3489130421. The cubic root of 180072 is about 56.4696890175.

Subtracting 180072 from its reverse (270081), we obtain a palindrome (90009).

It can be divided in two parts, 1800 and 72, that multiplied together give a square (129600 = 3602).

The spelling of 180072 in words is "one hundred eighty thousand, seventy-two".

Divisors: 1 2 3 4 6 8 9 12 18 24 36 41 61 72 82 122 123 164 183 244 246 328 366 369 488 492 549 732 738 984 1098 1464 1476 2196 2501 2952 4392 5002 7503 10004 15006 20008 22509 30012 45018 60024 90036 180072