40145216140800 has 720 divisors, whose sum is σ = 152209780763040. Its totient is φ = 10069699461120.

The previous prime is 40145216140793. The next prime is 40145216140807. The reversal of 40145216140800 is 804161254104.

40145216140800 is a `hidden beast` number, since 4 + 0 + 1 + 452 + 161 + 40 + 8 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (40145216140793) and next prime (40145216140807).

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×40145216140800² (a number of 28 digits) contains 22 as substring.

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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 (40145216140807) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 3973588549 + ... + 3973598651.

It is an arithmetic number, because the mean of its divisors is an integer number (211402473282).

Almost surely, 2^{40145216140800} is an apocalyptic number.

40145216140800 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 40145216140800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (76104890381520).

40145216140800 is an abundant number, since it is smaller than the sum of its proper divisors (112064564622240).

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

40145216140800 is a wasteful number, since it uses less digits than its factorization.

40145216140800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12183 (or 12159 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

Adding to 40145216140800 its reverse (804161254104), we get a palindrome (40949377394904).

The spelling of 40145216140800 in words is "forty trillion, one hundred forty-five billion, two hundred sixteen million, one hundred forty thousand, eight hundred".