468753120 has 288 divisors, whose sum is σ = 1768332384. Its totient is φ = 112128000.

The previous prime is 468753119. The next prime is 468753127. The reversal of 468753120 is 21357864.

468753120 is a `hidden beast` number, since 46 + 87 + 531 + 2 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (468753127) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1599694 + ... + 1599986.

It is an arithmetic number, because the mean of its divisors is an integer number (6140043).

Almost surely, 2^468753120 is an apocalyptic number.

468753120 is a gapful number since it is divisible by the number (40) 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 468753120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (884166192).

468753120 is an abundant number, since it is smaller than the sum of its proper divisors (1299579264).

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

468753120 is a wasteful number, since it uses less digits than its factorization.

468753120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 426 (or 415 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The square root of 468753120 is about 21650.7071478047. The cubic root of 468753120 is about 776.8098499629.

The spelling of 468753120 in words is "four hundred sixty-eight million, seven hundred fifty-three thousand, one hundred twenty".