414144 has 42 divisors (see below), whose sum is σ = 1188720. Its totient is φ = 137856.

The previous prime is 414131. The next prime is 414157. The reversal of 414144 is 441414.

It is an interprime number because it is at equal distance from previous prime (414131) and next prime (414157).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 217 + ... + 935.

2⁴¹⁴¹⁴⁴ 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 414144, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (594360).

414144 is an abundant number, since it is smaller than the sum of its proper divisors (774576).

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

414144 is a wasteful number, since it uses less digits than its factorization.

414144 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 737 (or 724 counting only the distinct ones).

The product of its digits is 256, while the sum is 18.

The square root of 414144 is about 643.5402085340. The cubic root of 414144 is about 74.5390393412.

Adding to 414144 its reverse (441414), we get a palindrome (855558).

The spelling of 414144 in words is "four hundred fourteen thousand, one hundred forty-four", and thus it is an iban number.