403872 has 48 divisors (see below), whose sum is σ = 1213632. Its totient is φ = 115200.

The previous prime is 403867. The next prime is 403877. The reversal of 403872 is 278304.

It is an interprime number because it is at equal distance from previous prime (403867) and next prime (403877).

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

It is a super-2 number, since 2×403872² = 326225184768, which contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (403877) by changing a digit.

403872 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 (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 372 + ... + 972.

It is an arithmetic number, because the mean of its divisors is an integer number (25284).

2⁴⁰³⁸⁷² is an apocalyptic number.

403872 is a gapful number since it is divisible by the number (42) 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 403872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (606816).

403872 is an abundant number, since it is smaller than the sum of its proper divisors (809760).

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

403872 is a wasteful number, since it uses less digits than its factorization.

403872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 621 (or 613 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 24.

The square root of 403872 is about 635.5092446220. The cubic root of 403872 is about 73.9176097876.

It can be divided in two parts, 403 and 872, that added together give a triangular number (1275 = T₅₀).

The spelling of 403872 in words is "four hundred three thousand, eight hundred seventy-two".