393472 has 36 divisors (see below), whose sum is σ = 827820. Its totient is φ = 186368.

The previous prime is 393451. The next prime is 393473. The reversal of 393472 is 274393.

393472 is nontrivially palindromic in base 15.

It can be written as a sum of positive squares in 2 ways, for example, as 246016 + 147456 = 496^2 + 384^2 .

Its product of digits (4536) is a multiple of the sum of its prime divisors (84).

It is a plaindrome in base 6.

It is a self number, because there is not a number n which added to its sum of digits gives 393472.

It is not an unprimeable number, because it can be changed into a prime (393473) by changing a digit.

393472 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 7398 + ... + 7450.

It is an arithmetic number, because the mean of its divisors is an integer number (22995).

2³⁹³⁴⁷² is an apocalyptic number.

393472 is a gapful number since it is divisible by the number (32) 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 393472, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (413910).

393472 is an abundant number, since it is smaller than the sum of its proper divisors (434348).

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

393472 is an equidigital number, since it uses as much as digits as its factorization.

393472 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 84 counting only the distinct ones).

The product of its digits is 4536, while the sum is 28.

The square root of 393472 is about 627.2734650852. The cubic root of 393472 is about 73.2776068833.

The spelling of 393472 in words is "three hundred ninety-three thousand, four hundred seventy-two".