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54000 = 243353
BaseRepresentation
bin1101001011110000
32202002000
431023300
53212000
61054000
7313302
oct151360
982060
1054000
1137631
1227300
131b76b
1415972
1511000
hexd2f0

54000 has 80 divisors (see below), whose sum is σ = 193440. Its totient is φ = 14400.

The previous prime is 53993. The next prime is 54001. The reversal of 54000 is 45.

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.

54000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (80).

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

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 10 and base 15.

It is a zygodrome in base 15.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (54001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 10798 + ... + 10802.

It is an arithmetic number, because the mean of its divisors is an integer number (2418).

254000 is an apocalyptic number.

54000 is a gapful number since it is divisible by the number (50) 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 54000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (96720).

54000 is an abundant number, since it is smaller than the sum of its proper divisors (139440).

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

54000 is a wasteful number, since it uses less digits than its factorization.

54000 is an evil number, because the sum of its binary digits is even.

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

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 54000 is about 232.3790007724. The cubic root of 54000 is about 37.7976314968.

Adding to 54000 its reverse (45), we get a palindrome (54045).

It can be divided in two parts, 5 and 4000, that added together give a triangular number (4005 = T89).

The spelling of 54000 in words is "fifty-four thousand", and thus it is an eban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 36 40 45 48 50 54 60 72 75 80 90 100 108 120 125 135 144 150 180 200 216 225 240 250 270 300 360 375 400 432 450 500 540 600 675 720 750 900 1000 1080 1125 1200 1350 1500 1800 2000 2160 2250 2700 3000 3375 3600 4500 5400 6000 6750 9000 10800 13500 18000 27000 54000