414880 has 24 divisors (see below), whose sum is σ = 980532. Its totient is φ = 165888.

The previous prime is 414871. The next prime is 414889. The reversal of 414880 is 88414.

It is an interprime number because it is at equal distance from previous prime (414871) and next prime (414889).

It can be written as a sum of positive squares in 2 ways, for example, as 414736 + 144 = 644^2 + 12^2 .

It is a plaindrome in base 13.

It is not an unprimeable number, because it can be changed into a prime (414889) by changing a digit.

414880 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 3 ways as a sum of consecutive naturals, for example, 1137 + ... + 1456.

2⁴¹⁴⁸⁸⁰ is an apocalyptic number.

414880 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

414880 is an abundant number, since it is smaller than the sum of its proper divisors (565652).

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

414880 is a wasteful number, since it uses less digits than its factorization.

414880 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2608 (or 2600 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 25.

The square root of 414880 is about 644.1117915393. Note that the first 3 decimals coincide. The cubic root of 414880 is about 74.5831691336.

It can be divided in two parts, 4 and 14880, that added together give a square (14884 = 122²).

The spelling of 414880 in words is "four hundred fourteen thousand, eight hundred eighty".