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72900 = 223652
BaseRepresentation
bin10001110011000100
310201000000
4101303010
54313100
61321300
7422352
oct216304
9121000
1072900
114a853
1236230
1327249
141c7d2
1516900
hex11cc4

72900 has 63 divisors (see below), whose sum is σ = 237181. Its totient is φ = 19440.

The previous prime is 72893. The next prime is 72901. The reversal of 72900 is 927.

72900 = T269 + T270.

The square root of 72900 is 270.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 26244 + 46656 = 162^2 + 216^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (72901) by changing a digit.

72900 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 (7) of ones.

It is a polite number, since it can be written in 20 ways as a sum of consecutive naturals, for example, 14578 + ... + 14582.

272900 is an apocalyptic number.

72900 is the 270-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72900

72900 is an abundant number, since it is smaller than the sum of its proper divisors (164281).

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

72900 is a wasteful number, since it uses less digits than its factorization.

72900 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 32 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 126, while the sum is 18.

The cubic root of 72900 is about 41.7742995025.

The spelling of 72900 in words is "seventy-two thousand, nine hundred".

Divisors: 1 2 3 4 5 6 9 10 12 15 18 20 25 27 30 36 45 50 54 60 75 81 90 100 108 135 150 162 180 225 243 270 300 324 405 450 486 540 675 729 810 900 972 1215 1350 1458 1620 2025 2430 2700 2916 3645 4050 4860 6075 7290 8100 12150 14580 18225 24300 36450 72900