47628 has 54 divisors (see below), whose sum is σ = 145236. Its totient is φ = 13608.

The previous prime is 47623. The next prime is 47629. The reversal of 47628 is 82674.

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 is a tau number, because it is divible by the number of its divisors (54).

It is a Harshad number since it is a multiple of its sum of digits (27).

Its product of digits (2688) is a multiple of the sum of its prime divisors (12).

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 47628.

It is not an unprimeable number, because it can be changed into a prime (47623) by changing a digit.

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 17 ways as a sum of consecutive naturals, for example, 6801 + ... + 6807.

2^{47628} 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 47628, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (72618).

47628 is an abundant number, since it is smaller than the sum of its proper divisors (97608).

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

47628 is a wasteful number, since it uses less digits than its factorization.

47628 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 33 (or 12 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 47628 is about 218.2384017537. The cubic root of 47628 is about 36.2482837079.

Multiplying 47628 by its sum of digits (27), we get a square (1285956 = 1134^{2}).

47628 divided by its sum of digits (27) gives a square (1764 = 42^{2}).

Multiplying 47628 by its product of digits (2688), we get a cube (128024064 = 504^{3}).

The spelling of 47628 in words is "forty-seven thousand, six hundred twenty-eight".

Divisors: 1 2 3 4 6 7 9 12 14 18 21 27 28 36 42 49 54 63 81 84 98 108 126 147 162 189 196 243 252 294 324 378 441 486 567 588 756 882 972 1134 1323 1701 1764 2268 2646 3402 3969 5292 6804 7938 11907 15876 23814 47628

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