814414029714000 has 400 divisors, whose sum is σ = 2968712158423440. Its totient is φ = 215184619699200.

The previous prime is 814414029713983. The next prime is 814414029714049. The reversal of 814414029714000 is 417920414418.

814414029714000 is a `hidden beast` number, since 8 + 1 + 4 + 414 + 0 + 2 + 97 + 140 + 0 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 27556326345744 + 786857703368256 = 5249412^2 + 28050984^2 .

It is a tau number, because it is divible by the number of its divisors (400).

It is a hoax number, since the sum of its digits (45) 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 (45).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 5402767 + ... + 40718766.

Almost surely, 2^{814414029714000} is an apocalyptic number.

814414029714000 is a gapful number since it is divisible by the number (80) 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 814414029714000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1484356079211720).

814414029714000 is an abundant number, since it is smaller than the sum of its proper divisors (2154298128709440).

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

814414029714000 is a wasteful number, since it uses less digits than its factorization.

814414029714000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 46121677 (or 46121652 counting only the distinct ones).

The product of its (nonzero) digits is 258048, while the sum is 45.

The spelling of 814414029714000 in words is "eight hundred fourteen trillion, four hundred fourteen billion, twenty-nine million, seven hundred fourteen thousand".