51585984 has 168 divisors, whose sum is σ = 159763968. Its totient is φ = 16485120.

The previous prime is 51585949. The next prime is 51585991. The reversal of 51585984 is 48958515.

It is a happy number.

51585984 is a `hidden beast` number, since 5 + 1 + 58 + 598 + 4 = 666.

It is a super-2 number, since 2×51585984² = 5322227490496512, which contains 22 as substring.

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, 482059 + ... + 482165.

It is an arithmetic number, because the mean of its divisors is an integer number (950976).

Almost surely, 2^51585984 is an apocalyptic number.

51585984 is a gapful number since it is divisible by the number (54) 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 51585984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (79881984).

51585984 is an abundant number, since it is smaller than the sum of its proper divisors (108177984).

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

51585984 is a wasteful number, since it uses less digits than its factorization.

51585984 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 165 (or 143 counting only the distinct ones).

The product of its digits is 288000, while the sum is 45.

The square root of 51585984 is about 7182.3383378953. The cubic root of 51585984 is about 372.2578856978.

The spelling of 51585984 in words is "fifty-one million, five hundred eighty-five thousand, nine hundred eighty-four".