51264000 has 240 divisors, whose sum is σ = 186717960. Its totient is φ = 13516800.

The previous prime is 51263999. The next prime is 51264013. The reversal of 51264000 is 46215.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 8020224 + 43243776 = 2832^2 + 6576^2 .

It is a tau number, because it is divible by the number of its divisors (240).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 575956 + ... + 576044.

Almost surely, 2^51264000 is an apocalyptic number.

51264000 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 51264000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (93358980).

51264000 is an abundant number, since it is smaller than the sum of its proper divisors (135453960).

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

51264000 is an equidigital number, since it uses as much as digits as its factorization.

51264000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 99 counting only the distinct ones).

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

The square root of 51264000 is about 7159.8882672846. Note that the first 3 decimals coincide. The cubic root of 51264000 is about 371.4817618950.

It can be divided in two parts, 512 and 64000, that multiplied together give a cube (32768000 = 320³).

The spelling of 51264000 in words is "fifty-one million, two hundred sixty-four thousand".