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206 is both a nontotient and a noncototient. [1] 206 is an untouchable number. [2] It is the lowest positive integer (when written in English as "two hundred and six") to employ all of the vowels once only, not including Y. The other numbers sharing this property are 230, 250, 260, 602, 640, 5000, 8000, 9000, 26,000, 80,000 and 90,000.
The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...
a prime number has only 1 and itself as divisors; that is, d(n) = 2; a composite number has more than just 1 and itself as divisors; that is, d(n) > 2; a highly composite number has a number of positive divisors that is greater than any lesser number; that is, d(n) > d(m) for every positive integer m < n.
The number 5 is untouchable, as it is not the sum of the proper divisors of any positive integer: 5 = 1 + 4 is the only way to write 5 as the sum of distinct positive integers including 1, but if 4 divides a number, 2 does also, so 1 + 4 cannot be the sum of all of any number's proper divisors (since the list of factors would have to contain ...
25 206: 1.205 703 438 × 10 100 ... For instance, the number of ways to choose all ... is divisible by if and only if is a prime number. [52] For any given integer ...
360 is divisible by the number of its divisors , and it is the smallest number divisible by every natural number from 1 to 10, except 7. Furthermore, one of the divisors of 360 is 72, which is the number of primes below it. 360 is the sum of twin primes (179 + 181) and the sum of four consecutive powers of three (9 + 27 + 81 + 243).
12 (twelve) is the natural number following 11 and preceding 13.. Twelve is the 3rd superior highly composite number, [1] the 3rd colossally abundant number, [2] the 5th highly composite number, and is divisible by the numbers from 1 to 4, and 6, a large number of divisors comparatively.
First, the digits of the number being tested are grouped in blocks of three. The odd numbered groups are summed. The sum of the even numbered groups is then subtracted from the sum of the odd numbered groups. The test number is divisible by 7, 11 or 13 iff the result of the summation is divisible by 7, 11 or 13 respectively. [2] [3] Example: