414100000 has 144 divisors (see below), whose sum is σ = 1054198152. Its totient is φ = 160000000.

The previous prime is 414099997. The next prime is 414100061. The reversal of 414100000 is 1414.

It can be written as a sum of positive squares in 12 ways, for example, as 186814224 + 227285776 = 13668^2 + 15076^2 .

It is a Harshad number since it is a multiple of its sum of digits (10).

It is a self number, because there is not a number n which added to its sum of digits gives 414100000.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 4099950 + ... + 4100050.

Almost surely, 2^414100000 is an apocalyptic number.

414100000 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 414100000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (527099076).

414100000 is an abundant number, since it is smaller than the sum of its proper divisors (640098152).

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

414100000 is an equidigital number, since it uses as much as digits as its factorization.

414100000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 177 (or 149 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 10.

The square root of 414100000 is about 20349.4471669380. The cubic root of 414100000 is about 745.3639949140.

Adding to 414100000 its reverse (1414), we get a palindrome (414101414).

The spelling of 414100000 in words is "four hundred fourteen million, one hundred thousand".