414134202400000 has 432 divisors, whose sum is σ = 1037666652302448. Its totient is φ = 164946862080000.

The previous prime is 414134202399991. The next prime is 414134202400001. The reversal of 414134202400000 is 4202431414.

It can be written as a sum of positive squares in 24 ways, for example, as 412046477949184 + 2087724450816 = 20298928^2 + 1444896^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414134202400001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 347136799404 + ... + 347136800596.

It is an arithmetic number, because the mean of its divisors is an integer number (2402006139589).

Almost surely, 2^{414134202400000} is an apocalyptic number.

414134202400000 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 414134202400000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (518833326151224).

414134202400000 is an abundant number, since it is smaller than the sum of its proper divisors (623532449902448).

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

414134202400000 is an equidigital number, since it uses as much as digits as its factorization.

414134202400000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2724 (or 2690 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 25.

Adding to 414134202400000 its reverse (4202431414), we get a palindrome (414138404831414).

The spelling of 414134202400000 in words is "four hundred fourteen trillion, one hundred thirty-four billion, two hundred two million, four hundred thousand".