648516418804800 has 7560 divisors, whose sum is σ = 3162725440205760. Its totient is φ = 129721297305600.

The previous prime is 648516418804789. The next prime is 648516418804811. The reversal of 648516418804800 is 8408814615846.

648516418804800 is a `hidden beast` number, since 6 + 4 + 8 + 5 + 1 + 64 + 18 + 80 + 480 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (648516418804789) and next prime (648516418804811).

It is a tau number, because it is divible by the number of its divisors (7560).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 1079 ways as a sum of consecutive naturals, for example, 2085261796645 + ... + 2085261796955.

Almost surely, 2^{648516418804800} is an apocalyptic number.

648516418804800 is a gapful number since it is divisible by the number (60) 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 648516418804800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1581362720102880).

648516418804800 is an abundant number, since it is smaller than the sum of its proper divisors (2514209021400960).

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

648516418804800 is a wasteful number, since it uses less digits than its factorization.

648516418804800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 481 (or 437 counting only the distinct ones).

The product of its (nonzero) digits is 47185920, while the sum is 63.

The spelling of 648516418804800 in words is "six hundred forty-eight trillion, five hundred sixteen billion, four hundred eighteen million, eight hundred four thousand, eight hundred".