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72000 = 263253
BaseRepresentation
bin10001100101000000
310122202200
4101211000
54301000
61313200
7416625
oct214500
9118680
1072000
114a105
1235800
1326a06
141c34c
1516500
hex11940

72000 has 84 divisors (see below), whose sum is σ = 257556. Its totient is φ = 19200.

The previous prime is 71999. The next prime is 72019. The reversal of 72000 is 27.

Adding to 72000 its reverse (27), we get a palindrome (72027).

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 2304 + 69696 = 48^2 + 264^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a nialpdrome in base 10.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 14398 + ... + 14402.

272000 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 72000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (128778).

72000 is an abundant number, since it is smaller than the sum of its proper divisors (185556).

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

72000 is a wasteful number, since it uses less digits than its factorization.

72000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 33 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 14, while the sum is 9.

The square root of 72000 is about 268.3281573000. The cubic root of 72000 is about 41.6016764610.

The spelling of 72000 in words is "seventy-two thousand", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 45 48 50 60 64 72 75 80 90 96 100 120 125 144 150 160 180 192 200 225 240 250 288 300 320 360 375 400 450 480 500 576 600 720 750 800 900 960 1000 1125 1200 1440 1500 1600 1800 2000 2250 2400 2880 3000 3600 4000 4500 4800 6000 7200 8000 9000 12000 14400 18000 24000 36000 72000