415440 has 60 divisors (see below), whose sum is σ = 1397604. Its totient is φ = 110592.

The previous prime is 415427. The next prime is 415447. The reversal of 415440 is 44514.

It can be written as a sum of positive squares in 2 ways, for example, as 318096 + 97344 = 564^2 + 312^2 .

It is a tau number, because it is divible by the number of its divisors (60).

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

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415447) by changing a digit.

415440 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 432 + ... + 1008.

2⁴¹⁵⁴⁴⁰ is an apocalyptic number.

415440 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 415440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (698802).

415440 is an abundant number, since it is smaller than the sum of its proper divisors (982164).

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

415440 is a wasteful number, since it uses less digits than its factorization.

415440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 596 (or 587 counting only the distinct ones).

The product of its (nonzero) digits is 320, while the sum is 18.

The square root of 415440 is about 644.5463520958. The cubic root of 415440 is about 74.6167111994.

Adding to 415440 its reverse (44514), we get a palindrome (459954).

The spelling of 415440 in words is "four hundred fifteen thousand, four hundred forty".