21624 has 32 divisors (see below), whose sum is σ = 58320. Its totient is φ = 6656.

The previous prime is 21617. The next prime is 21647. The reversal of 21624 is 42612.

21624 is nontrivially palindromic in base 7.

It is a super-3 number, since 3×21624^{3} = 30333976975872, which contains 333 as substring.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable 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, 382 + ... + 434.

2^{21624} is an apocalyptic number.

21624 is a gapful number since it is divisible by the number (24) 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 21624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (29160).

21624 is an abundant number, since it is smaller than the sum of its proper divisors (36696).

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

21624 is a wasteful number, since it uses less digits than its factorization.

21624 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 79 (or 75 counting only the distinct ones).

The product of its digits is 96, while the sum is 15.

The square root of 21624 is about 147.0510115572. The cubic root of 21624 is about 27.8598438256.

Subtracting from 21624 its sum of digits (15), we obtain a square (21609 = 147^{2}).

Subtracting from 21624 its product of digits (96), we obtain a triangular number (21528 = T_{207}).

It can be divided in two parts, 216 and 24, that multiplied together give a square (5184 = 72^{2}).

The spelling of 21624 in words is "twenty-one thousand, six hundred twenty-four".

Divisors: 1 2 3 4 6 8 12 17 24 34 51 53 68 102 106 136 159 204 212 318 408 424 636 901 1272 1802 2703 3604 5406 7208 10812 21624

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