406752 has 48 divisors (see below), whose sum is σ = 1128960. Its totient is φ = 127872.

The previous prime is 406739. The next prime is 406789. The reversal of 406752 is 257604.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (48).

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

It is a congruent number.

It is an unprimeable number.

406752 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 7 ways as a sum of consecutive naturals, for example, 1713 + ... + 1935.

It is an arithmetic number, because the mean of its divisors is an integer number (23520).

2⁴⁰⁶⁷⁵² 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 406752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (564480).

406752 is an abundant number, since it is smaller than the sum of its proper divisors (722208).

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

406752 is a wasteful number, since it uses less digits than its factorization.

406752 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 255 (or 247 counting only the distinct ones).

The product of its (nonzero) digits is 1680, while the sum is 24.

The square root of 406752 is about 637.7711188193. The cubic root of 406752 is about 74.0928952668.

The spelling of 406752 in words is "four hundred six thousand, seven hundred fifty-two".