40448582406400 has 729 divisors, whose sum is σ = 119804445050157. Its totient is φ = 13480995225600.

The previous prime is 40448582406347. The next prime is 40448582406493. The reversal of 40448582406400 is 460428584404.

The square root of 40448582406400 is 6359920.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 13 ways, for example, as 37405260288256 + 3043322118144 = 6115984^2 + 1744512^2 .

It is a super-2 number, since 2×40448582406400² (a number of 28 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (49).

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 146023763062 + ... + 146023763338.

Almost surely, 2^{40448582406400} is an apocalyptic number.

40448582406400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

40448582406400 is the 6359920-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 40448582406400

40448582406400 is an abundant number, since it is smaller than the sum of its proper divisors (79355862643757).

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

40448582406400 is an frugal number, since it uses more digits than its factorization.

40448582406400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 676 (or 332 counting only the distinct ones).

The product of its (nonzero) digits is 3932160, while the sum is 49.

40448582406400 divided by its sum of digits (49) gives a square (825481273600 = 908560²).

The spelling of 40448582406400 in words is "forty trillion, four hundred forty-eight billion, five hundred eighty-two million, four hundred six thousand, four hundred".