6456746390400 has 2304 divisors, whose sum is σ = 26672440354560. Its totient is φ = 1535034654720.

The previous prime is 6456746390389. The next prime is 6456746390401. The reversal of 6456746390400 is 40936476546.

It is a happy number.

6456746390400 is a `hidden beast` number, since 6 + 4 + 56 + 7 + 463 + 90 + 40 + 0 = 666.

It is a super-3 number, since 3×6456746390400³ (a number of 39 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (6456746390401) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 21031747047 + ... + 21031747353.

It is an arithmetic number, because the mean of its divisors is an integer number (11576580015).

Almost surely, 2^{6456746390400} is an apocalyptic number.

6456746390400 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 6456746390400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13336220177280).

6456746390400 is an abundant number, since it is smaller than the sum of its proper divisors (20215693964160).

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

6456746390400 is a wasteful number, since it uses less digits than its factorization.

6456746390400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 443 (or 414 counting only the distinct ones).

The product of its (nonzero) digits is 13063680, while the sum is 54.

The spelling of 6456746390400 in words is "six trillion, four hundred fifty-six billion, seven hundred forty-six million, three hundred ninety thousand, four hundred".