414972 has 18 divisors (see below), whose sum is σ = 1049048. Its totient is φ = 138312.

The previous prime is 414971. The next prime is 414977. The reversal of 414972 is 279414.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (18).

It is a plaindrome in base 7.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 414972.

It is not an unprimeable number, because it can be changed into a prime (414971) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 5728 + ... + 5799.

2⁴¹⁴⁹⁷² is an apocalyptic number.

It is an amenable number.

414972 is an abundant number, since it is smaller than the sum of its proper divisors (634076).

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

414972 is a wasteful number, since it uses less digits than its factorization.

414972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11537 (or 11532 counting only the distinct ones).

The product of its digits is 2016, while the sum is 27.

The square root of 414972 is about 644.1832037550. The cubic root of 414972 is about 74.5886816870.

The spelling of 414972 in words is "four hundred fourteen thousand, nine hundred seventy-two".