51854400 has 252 divisors, whose sum is σ = 199196452. Its totient is φ = 12718080.

The previous prime is 51854389. The next prime is 51854417. The reversal of 51854400 is 445815.

It is a Cunningham number, because it is equal to 7201²-1.

It can be written as a sum of positive squares in 6 ways, for example, as 12616704 + 39237696 = 3552^2 + 6264^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 187062 + ... + 187338.

Almost surely, 2^51854400 is an apocalyptic number.

51854400 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 51854400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (99598226).

51854400 is an abundant number, since it is smaller than the sum of its proper divisors (147342052).

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

51854400 is a wasteful number, since it uses less digits than its factorization.

51854400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 318 (or 300 counting only the distinct ones).

The product of its (nonzero) digits is 3200, while the sum is 27.

The square root of 51854400 is about 7200.9999305652. Note that the first 4 decimals coincide. The cubic root of 51854400 is about 372.9024223238.

The spelling of 51854400 in words is "fifty-one million, eight hundred fifty-four thousand, four hundred".