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198432 = 25321353
BaseRepresentation
bin110000011100100000
3101002012100
4300130200
522322212
64130400
71454343
oct603440
9332170
10198432
111260a3
1296a00
136c420
145245a
153dbdc
hex30720

198432 has 72 divisors (see below), whose sum is σ = 619164. Its totient is φ = 59904.

The previous prime is 198427. The next prime is 198437. The reversal of 198432 is 234891.

It can be divided in two parts, 1984 and 32, that added together give a triangular number (2016 = T63).

It is an interprime number because it is at equal distance from previous prime (198427) and next prime (198437).

It can be written as a sum of positive squares in 2 ways, for example, as 197136 + 1296 = 444^2 + 36^2 .

It is a tau number, because it is divible by the number of its divisors (72).

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 junction number, because it is equal to n+sod(n) for n = 198396 and 198405.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 198432.

It is not an unprimeable number, because it can be changed into a prime (198437) by changing a digit.

198432 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, 3718 + ... + 3770.

2198432 is an apocalyptic number.

198432 is a gapful number since it is divisible by the number (12) 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 198432, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (309582).

198432 is an abundant number, since it is smaller than the sum of its proper divisors (420732).

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

198432 is a wasteful number, since it uses less digits than its factorization.

198432 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 82 (or 71 counting only the distinct ones).

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

The square root of 198432 is about 445.4570686385. The cubic root of 198432 is about 58.3271249629.

The spelling of 198432 in words is "one hundred ninety-eight thousand, four hundred thirty-two".

Divisors: 1 2 3 4 6 8 9 12 13 16 18 24 26 32 36 39 48 52 53 72 78 96 104 106 117 144 156 159 208 212 234 288 312 318 416 424 468 477 624 636 689 848 936 954 1248 1272 1378 1696 1872 1908 2067 2544 2756 3744 3816 4134 5088 5512 6201 7632 8268 11024 12402 15264 16536 22048 24804 33072 49608 66144 99216 198432