51264 has 42 divisors (see below), whose sum is σ = 148590. Its totient is φ = 16896.

The previous prime is 51263. The next prime is 51283. The reversal of 51264 is 46215.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 36864 + 14400 = 192^2 + 120^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (51263) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 532 + ... + 620.

2⁵¹²⁶⁴ 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 51264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (74295).

51264 is an abundant number, since it is smaller than the sum of its proper divisors (97326).

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

51264 is a wasteful number, since it uses less digits than its factorization.

51264 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 107 (or 94 counting only the distinct ones).

The product of its digits is 240, while the sum is 18.

The square root of 51264 is about 226.4155471694. The cubic root of 51264 is about 37.1481761895.

Adding to 51264 its reverse (46215), we get a palindrome (97479).

It can be divided in two parts, 512 and 64, that multiplied together give a 15-th power (32768 = 2¹⁵).

The spelling of 51264 in words is "fifty-one thousand, two hundred sixty-four".