51648000 has 160 divisors (see below), whose sum is σ = 172355040. Its totient is φ = 13721600.

The previous prime is 51647983. The next prime is 51648007. The reversal of 51648000 is 84615.

It is a tau number, because it is divible by the number of its divisors (160).

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 (51648007) 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 15 ways as a sum of consecutive naturals, for example, 191866 + ... + 192134.

It is an arithmetic number, because the mean of its divisors is an integer number (1077219).

Almost surely, 2^51648000 is an apocalyptic number.

51648000 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 51648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (86177520).

51648000 is an abundant number, since it is smaller than the sum of its proper divisors (120707040).

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

51648000 is an equidigital number, since it uses as much as digits as its factorization.

51648000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 305 (or 279 counting only the distinct ones).

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

The square root of 51648000 is about 7186.6542980722. The cubic root of 51648000 is about 372.4070004910.

It can be divided in two parts, 516 and 48000, that added together give a triangular number (48516 = T₃₁₁).

The spelling of 51648000 in words is "fifty-one million, six hundred forty-eight thousand".