4509460800 has 756 divisors, whose sum is σ = 18544923540. Its totient is φ = 1035141120.

The previous prime is 4509460777. The next prime is 4509460831. The reversal of 4509460800 is 80649054.

4509460800 is a `hidden beast` number, since 45 + 0 + 9 + 4 + 608 + 0 + 0 = 666.

It can be written as a sum of positive squares in 18 ways, for example, as 3465912384 + 1043548416 = 58872^2 + 32304^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 41371146 + ... + 41371254.

Almost surely, 2^4509460800 is an apocalyptic number.

4509460800 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 4509460800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9272461770).

4509460800 is an abundant number, since it is smaller than the sum of its proper divisors (14035462740).

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

4509460800 is a wasteful number, since it uses less digits than its factorization.

4509460800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 180 (or 149 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The square root of 4509460800 is about 67152.5189400964. The cubic root of 4509460800 is about 1652.1198098787.

The spelling of 4509460800 in words is "four billion, five hundred nine million, four hundred sixty thousand, eight hundred".