407968 has 48 divisors (see below), whose sum is σ = 937440. Its totient is φ = 172800.

The previous prime is 407959. The next prime is 407969. The reversal of 407968 is 869704.

It is an Ulam number.

It is not an unprimeable number, because it can be changed into a prime (407969) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 6658 + ... + 6718.

It is an arithmetic number, because the mean of its divisors is an integer number (19530).

2⁴⁰⁷⁹⁶⁸ 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 407968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (468720).

407968 is an abundant number, since it is smaller than the sum of its proper divisors (529472).

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

407968 is a wasteful number, since it uses less digits than its factorization.

407968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 101 (or 93 counting only the distinct ones).

The product of its (nonzero) digits is 12096, while the sum is 34.

The square root of 407968 is about 638.7237274440. The cubic root of 407968 is about 74.1666562864.

It can be divided in two parts, 40796 and 8, that added together give a palindrome (40804).

The spelling of 407968 in words is "four hundred seven thousand, nine hundred sixty-eight".