414364105066800 has 240 divisors, whose sum is σ = 1517342033894400. Its totient is φ = 94688396267520.

The previous prime is 414364105066759. The next prime is 414364105066837. The reversal of 414364105066800 is 8660501463414.

It is a tau number, because it is divible by the number of its divisors (240).

It is a super-2 number, since 2×414364105066800² (a number of 30 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 414364105066800.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 27920089 + ... + 40103111.

It is an arithmetic number, because the mean of its divisors is an integer number (6322258474560).

Almost surely, 2^{414364105066800} is an apocalyptic number.

414364105066800 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 414364105066800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (758671016947200).

414364105066800 is an abundant number, since it is smaller than the sum of its proper divisors (1102977928827600).

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

414364105066800 is a wasteful number, since it uses less digits than its factorization.

414364105066800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12187100 (or 12187089 counting only the distinct ones).

The product of its (nonzero) digits is 1658880, while the sum is 48.

The spelling of 414364105066800 in words is "four hundred fourteen trillion, three hundred sixty-four billion, one hundred five million, sixty-six thousand, eight hundred".