51648 has 28 divisors (see below), whose sum is σ = 137160. Its totient is φ = 17152.

The previous prime is 51647. The next prime is 51659. The reversal of 51648 is 84615.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (51647) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 58 + ... + 326.

2⁵¹⁶⁴⁸ 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 51648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (68580).

51648 is an abundant number, since it is smaller than the sum of its proper divisors (85512).

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

51648 is a wasteful number, since it uses less digits than its factorization.

51648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 284 (or 274 counting only the distinct ones).

The product of its digits is 960, while the sum is 24.

The square root of 51648 is about 227.2619633815. The cubic root of 51648 is about 37.2407000491.

It can be divided in two parts, 5 and 1648, that added together give a triangular number (1653 = T₅₇).

The spelling of 51648 in words is "fifty-one thousand, six hundred forty-eight".