51975 has 48 divisors (see below), whose sum is σ = 119040. Its totient is φ = 21600.

The previous prime is 51973. The next prime is 51977. The reversal of 51975 is 57915.

51975 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (51973) and next prime (51977).

It is not a de Polignac number, because 51975 - 2¹ = 51973 is a prime.

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

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

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 51975.

It is not an unprimeable number, because it can be changed into a prime (51971) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4720 + ... + 4730.

It is an arithmetic number, because the mean of its divisors is an integer number (2480).

2⁵¹⁹⁷⁵ is an apocalyptic number.

51975 is a gapful number since it is divisible by the number (55) formed by its first and last digit.

51975 is an abundant number, since it is smaller than the sum of its proper divisors (67065).

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 (59520).

51975 is a wasteful number, since it uses less digits than its factorization.

51975 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 37 (or 26 counting only the distinct ones).

The product of its digits is 1575, while the sum is 27.

The square root of 51975 is about 227.9802623036. The cubic root of 51975 is about 37.3191290209.

51975 divided by its product of digits (1575) gives a palindrome (33).

The spelling of 51975 in words is "fifty-one thousand, nine hundred seventy-five".