414960 has 160 divisors (see below), whose sum is σ = 1666560. Its totient is φ = 82944.

The previous prime is 414959. The next prime is 414971. The reversal of 414960 is 69414.

414960 = 98² + 99² + ... + 129².

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 414960.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 21831 + ... + 21849.

It is an arithmetic number, because the mean of its divisors is an integer number (10416).

2⁴¹⁴⁹⁶⁰ is an apocalyptic number.

414960 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 414960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (833280).

414960 is an abundant number, since it is smaller than the sum of its proper divisors (1251600).

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

414960 is a wasteful number, since it uses less digits than its factorization.

414960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 55 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The square root of 414960 is about 644.1738895671. The cubic root of 414960 is about 74.5879627045.

The spelling of 414960 in words is "four hundred fourteen thousand, nine hundred sixty".