414000142514400 has 576 divisors, whose sum is σ = 1455278558086080. Its totient is φ = 101623789977600.

The previous prime is 414000142514377. The next prime is 414000142514501. The reversal of 414000142514400 is 4415241000414.

It is a super-2 number, since 2×414000142514400² (a number of 30 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 17983574890 + ... + 17983597910.

It is an arithmetic number, because the mean of its divisors is an integer number (2526525274455).

Almost surely, 2^{414000142514400} is an apocalyptic number.

414000142514400 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 414000142514400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (727639279043040).

414000142514400 is an abundant number, since it is smaller than the sum of its proper divisors (1041278415571680).

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

414000142514400 is a wasteful number, since it uses less digits than its factorization.

414000142514400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 24639 (or 24626 counting only the distinct ones).

The product of its (nonzero) digits is 10240, while the sum is 30.

Adding to 414000142514400 its reverse (4415241000414), we get a palindrome (418415383514814).

The spelling of 414000142514400 in words is "four hundred fourteen trillion, one hundred forty-two million, five hundred fourteen thousand, four hundred".