412972 has 30 divisors (see below), whose sum is σ = 862708. Its totient is φ = 172872.

The previous prime is 412967. The next prime is 412987. The reversal of 412972 is 279214.

It is a nialpdrome in base 14.

It is an unprimeable number.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 9583 + ... + 9625.

412972 is a Friedman number, since it can be written as 172*(9-2)^4, using all its digits and the basic arithmetic operations.

2⁴¹²⁹⁷² 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 412972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (431354).

412972 is an abundant number, since it is smaller than the sum of its proper divisors (449736).

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

412972 is an equidigital number, since it uses as much as digits as its factorization.

412972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 52 counting only the distinct ones).

The product of its digits is 1008, while the sum is 25.

The square root of 412972 is about 642.6289753816. The cubic root of 412972 is about 74.4686593998.

The spelling of 412972 in words is "four hundred twelve thousand, nine hundred seventy-two".