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213984 = 2532743
BaseRepresentation
bin110100001111100000
3101212112100
4310033200
523321414
64330400
71550601
oct641740
9355470
10213984
11136851
12a3a00
1376524
1457da8
1543609
hex343e0

213984 has 36 divisors (see below), whose sum is σ = 609336. Its totient is φ = 71232.

The previous prime is 213977. The next prime is 213989. The reversal of 213984 is 489312.

It can be divided in two parts, 21 and 3984, that added together give a triangular number (4005 = T89).

It is a tau number, because it is divible by the number of its divisors (36).

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

It is one of the 548 Lynch-Bell numbers.

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 213984.

It is not an unprimeable number, because it can be changed into a prime (213989) by changing a digit.

213984 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 5 ways as a sum of consecutive naturals, for example, 84 + ... + 659.

It is an arithmetic number, because the mean of its divisors is an integer number (16926).

2213984 is an apocalyptic number.

213984 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 213984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (304668).

213984 is an abundant number, since it is smaller than the sum of its proper divisors (395352).

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

213984 is a wasteful number, since it uses less digits than its factorization.

213984 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 759 (or 748 counting only the distinct ones).

The product of its digits is 1728, while the sum is 27.

The square root of 213984 is about 462.5840464175. The cubic root of 213984 is about 59.8127495625.

The spelling of 213984 in words is "two hundred thirteen thousand, nine hundred eighty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 72 96 144 288 743 1486 2229 2972 4458 5944 6687 8916 11888 13374 17832 23776 26748 35664 53496 71328 106992 213984