363840 has 56 divisors (see below), whose sum is σ = 1158240. Its totient is φ = 96768.

The previous prime is 363833. The next prime is 363841. The reversal of 363840 is 48363.

363840 = T₁₀₄ + T₁₀₅ + ... + T₁₄₈.

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

It is a self number, because there is not a number n which added to its sum of digits gives 363840.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 363840.

It is not an unprimeable number, because it can be changed into a prime (363841) by changing a digit.

363840 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, 771 + ... + 1149.

2³⁶³⁸⁴⁰ is an apocalyptic number.

363840 is a gapful number since it is divisible by the number (30) 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 363840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (579120).

363840 is an abundant number, since it is smaller than the sum of its proper divisors (794400).

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

363840 is a wasteful number, since it uses less digits than its factorization.

363840 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 399 (or 389 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 24.

The square root of 363840 is about 603.1915118766. The cubic root of 363840 is about 71.3899066934.

The spelling of 363840 in words is "three hundred sixty-three thousand, eight hundred forty".