414100 has 36 divisors (see below), whose sum is σ = 929628. Its totient is φ = 160000.

The previous prime is 414097. The next prime is 414101. The reversal of 414100 is 1414.

It can be written as a sum of positive squares in 6 ways, for example, as 7056 + 407044 = 84^2 + 638^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414101) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4050 + ... + 4150.

It is an arithmetic number, because the mean of its divisors is an integer number (25823).

2⁴¹⁴¹⁰⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (464814).

414100 is an abundant number, since it is smaller than the sum of its proper divisors (515528).

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

414100 is a wasteful number, since it uses less digits than its factorization.

414100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 156 (or 149 counting only the distinct ones).

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

The square root of 414100 is about 643.5060217278. The cubic root of 414100 is about 74.5363994914.

Adding to 414100 its reverse (1414), we get a palindrome (415514).

Subtracting from 414100 its reverse (1414), we obtain a triangular number (412686 = T₉₀₈).

It can be divided in two parts, 41 and 4100, that multiplied together give a square (168100 = 410²).

The spelling of 414100 in words is "four hundred fourteen thousand, one hundred", and thus it is an iban number.