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72180 = 22325401
BaseRepresentation
bin10001100111110100
310200000100
4101213310
54302210
61314100
7420303
oct214764
9120010
1072180
114a259
1235930
1326b14
141c43a
15165c0
hex119f4

72180 has 36 divisors (see below), whose sum is σ = 219492. Its totient is φ = 19200.

The previous prime is 72173. The next prime is 72211. The reversal of 72180 is 8127.

It can be written as a sum of positive squares in 2 ways, for example, as 54756 + 17424 = 234^2 + 132^2 .

It is a tau number, because it is divible by the number of its divisors (36).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 21 + ... + 380.

It is an arithmetic number, because the mean of its divisors is an integer number (6097).

272180 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 72180, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109746).

72180 is an abundant number, since it is smaller than the sum of its proper divisors (147312).

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

72180 is a wasteful number, since it uses less digits than its factorization.

72180 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 416 (or 411 counting only the distinct ones).

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

The square root of 72180 is about 268.6633581269. The cubic root of 72180 is about 41.6363156748.

It can be divided in two parts, 72 and 180, that added together give a palindrome (252).

The spelling of 72180 in words is "seventy-two thousand, one hundred eighty".

Divisors: 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 401 802 1203 1604 2005 2406 3609 4010 4812 6015 7218 8020 12030 14436 18045 24060 36090 72180