find the largest 3 digit number divisible by 16

WebA divisibility rule is a heuristic for determining whether a positive integer can be evenly divided by another (i.e. Thank you so much! So, 100015 is the least six-digit number exactly divisible by 83. A number is divisible by 6 if it is divisible by 2 and 3, i.e. Although not fully optimized, this solution it's pretty fast and I like how it works doing the task, so I didn't change it. still better than OP try generating all the number. The smallest three digit number divisible by 6 and 7 is = 42 3 = 126. Test for divisibility is done by, % calculating the least common multiplier for all digits, and testing. When the number 'a' is divisible by 'b' then it should give the remainder as zero. In hindsight, it is logical, it was bound to happen, so now I am looking for an alternative approach to accelerate this process and get my result sooner if possible. % generates a combination of digits to test, % remove N digits, and find remaining combinations. The 536 values found---all base 10 numbers that are divisible by their digits without repetition---are sorted descending, hence 9867312 is the greatest number divisible by its digits in base 10. The largest four digit number divisible by 42 is 9999 3 = 9996. Determine the largest 3-digit number which is exactly divisible by 8,10 and 12. Checking our work: 960/60=16, so yes, thats a multiple of 60. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. 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The largest or greatest 3-digit number divisible by 10 is the last number on the list above (last 3 digit number divisible Strictly by removing possibilities that cannot possibly work we are down to at most 7 digits. Now, the greatest four digit number is 9999. # Least common multiple of digits [1..15], # ------------------ GENERIC FUNCTIONS -------------------, # enumFromThenToNext:: Int -> Int -> Int -> Gen [Int], '''Non-finite series of integer values enumerated. I would be interested by further fair analysis if you take time to time it also. ;Here is an alternative version of power_up that could be more efficient as it does not repeatedly recalculate powers of the base. Not only A short comparison between the suggested solutions here. % temporarily store digit combinations here. ;deterimes the lcm least common multiple for a set of digits. the tests in a different order for maximum speed. % trials are stored highest values to lowest, % Precalculate all possible digit combinations, % Make an integer and check for divisibility, % precalc digit combos with length=NDigits, '''Largest number divisible by its digits''', # (Division by zero is not an option, so 0 and 5 are omitted), # Least common multiple of the digits above. Find the largest number (in a range) that has each digit exactly once and is divisible by 11, How terrifying is giving a conference talk? The number can not have a zero in it, that implies that it can not have a 5 either since if it has a 5, it must be divisible by 5, but the only numbers divisible by 5 end in 5 or 0. Then, we will take the required smallest 3-digit number as the first term, the required largest 3-digit number as the last term and 9 as the common difference of the A.P. While concise, the previous example is relatively slow, taking nearly 30 seconds to complete. answer answered Largest 3 digit number divisible by 16 Answer 14 people found it helpful Ankit1234 Hey friend! Soo -- try 62 * 16 ;Populate the primes sequence with the primes less than the current base. ;determines if a given number is exactly comprised of a given set of digits. Asking for help, clarification, or responding to other answers. if it is even and its sum and digits are divisible by 3. Simply added a counter and it takes that number of iterations until the desired number is reached, I know the number of iterations, as I checked afterwrards. Now we will divide the smallest 3-digit number with the LCM obtained, and the remainder will be subtracted from the dividend, and. This can be solved easily. On dividing 9999 by 360 we get 279 as remainder. To check Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. What should I do? */, /*curiosity's sake, track # of trials. This leaves 98764321. Required number = 999 3 = 996 So, 996 is the greatest 3 digit number. It passes all the test cases except one (blind case), and I have literally no idea what the issue is. 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So that leaves 98764321 as possible digits the number can contain. WebRepeat the process for larger numbers. 589). Ruling out 9- and 8-digit numbers (see first paragraph in the Raku example), we are looking for 7-digit numbers. So, 972 is the greatest 3-digit number which is divisible by 36. Largest number divisible by its digits From Rosetta Code Largest number divisible by its digits You are encouraged to according to the task description, using any The conditions are very easy to meet, thus there are many numbers that meet the requirements (I found more than 30k numbers that meet the criteria for the numbers where the leading number is 9). If a sum of digits is not divisible by 3 then the remainder should be either 1 or 2. The list monad can be derived by using a. function f which wraps its output in a list. NEXT TEST. Let's use the condition given in the question to find the required number. % whether a candidate can be divided by the LCM without remainder. (base ten) digits are all different (and do not include zero) and n is divisible by each of its individual digits. ;A container for the digits which are prime. Here is a stripped down version, as compared to the above, this may execute quicker. compared to the other solution ? */, /*does it contain a five or a zero? ;calculate the logarithm of the input in the current base. It is enemy divisible by 10 3. 999999 / 360 = 2777. Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960. So the maximum number possible will be 9876312, the last digit of two, since the result must be even. To check if the given number is exactly divisible by 11 follow the below steps Step 1: Find alternative digits in the given number and make 2 separate groups. Base 10 uses all digits but digit five and digit zero, base 16 uses all digits but digit zero. Digit four appears in six digit solutions. A number is divisible by 9 if its sum of digits is divisible by 9. The number should be an even number and sum of its digits should be Thank you for your valuable feedback! The integers here are too large (>= 2^53) to be accurately represented by Wren and so we follow the AWK approach of using an array of digits to represent them. ;Returns the smallest non-negative integer which contains each item from a given sequence exactly once as a digit. So, instead of simply moving on to a base 16 version, this next example is a fast version for arbitrary base. Thank you for your valuable feedback! A number is divisible by 18 if it is divisible by 2 and 9. Below is a list of all 3-digit EVEN numbers divisible by 16 in Connect and share knowledge within a single location that is structured and easy to search. Concept: Concept for Whole Numbers. % Find the largest integer divisible by all it's digits, with no digit repeated. 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