363972 has 36 divisors (see below), whose sum is σ = 989520. Its totient is φ = 103824.

The previous prime is 363967. The next prime is 363977. The reversal of 363972 is 279363.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (363967) and next prime (363977).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 363972.

It is not an unprimeable number, because it can be changed into a prime (363977) by changing a digit.

363972 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 11 ways as a sum of consecutive naturals, for example, 279 + ... + 897.

2³⁶³⁹⁷² 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 363972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (494760).

363972 is an abundant number, since it is smaller than the sum of its proper divisors (625548).

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

363972 is a wasteful number, since it uses less digits than its factorization.

363972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 640 (or 631 counting only the distinct ones).

The product of its digits is 6804, while the sum is 30.

The square root of 363972 is about 603.3009199396. The cubic root of 363972 is about 71.3985389936.

It can be divided in two parts, 363 and 972, that multiplied together give a square (352836 = 594²).

The spelling of 363972 in words is "three hundred sixty-three thousand, nine hundred seventy-two".