51765 has 32 divisors (see below), whose sum is σ = 103680. Its totient is φ = 21504.

The previous prime is 51749. The next prime is 51767. The reversal of 51765 is 56715.

51765 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It is not a de Polignac number, because 51765 - 2⁴ = 51749 is a prime.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 51765.

It is not an unprimeable number, because it can be changed into a prime (51767) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1771 + ... + 1799.

It is an arithmetic number, because the mean of its divisors is an integer number (3240).

2⁵¹⁷⁶⁵ is an apocalyptic number.

It is an amenable number.

51765 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (51840).

51765 is a wasteful number, since it uses less digits than its factorization.

51765 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61.

The product of its digits is 1050, while the sum is 24.

The square root of 51765 is about 227.5192299565. The cubic root of 51765 is about 37.2687997232.

Subtracting 51765 from its reverse (56715), we obtain a triangular number (4950 = T₉₉).

It can be divided in two parts, 5 and 1765, that added together give a triangular number (1770 = T₅₉).

The spelling of 51765 in words is "fifty-one thousand, seven hundred sixty-five".