414222000 has 320 divisors, whose sum is σ = 1470763008. Its totient is φ = 99840000.

The previous prime is 414221999. The next prime is 414222001. The reversal of 414222000 is 222414.

It is an interprime number because it is at equal distance from previous prime (414221999) and next prime (414222001).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is not an unprimeable number, because it can be changed into a prime (414222001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 3161935 + ... + 3162065.

Almost surely, 2^414222000 is an apocalyptic number.

414222000 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 414222000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (735381504).

414222000 is an abundant number, since it is smaller than the sum of its proper divisors (1056541008).

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

414222000 is a wasteful number, since it uses less digits than its factorization.

414222000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 205 (or 189 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 15.

The square root of 414222000 is about 20352.4445706161. Note that the first 3 decimals coincide. The cubic root of 414222000 is about 745.4371861550.

Adding to 414222000 its reverse (222414), we get a palindrome (414444414).

The spelling of 414222000 in words is "four hundred fourteen million, two hundred twenty-two thousand".