What is the greatest 5 digit even number
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To clarify, no digits can repeat either. Can someone outline their thought process to solve? Here's mine: I used a process of elimination to determine what numbers I could use in the ten-thousands, thousands, and hundreds place. This gave me $7 6 4$. Is this thought process safe so far? Where I think I began to mess up(if not earlier). I was left with $3$ and $1$. Choosing between $7 6 4 1 3$ and $7 6 4 3 1$, I made the unsafe assumption that division by $3$ would not be possible with a five-digit number ending with a $1$. Little did I know that $76431 /3 = 25477$. Aside from getting to this point and manually checking what's possible, can anyone explain a better approach?
R1w 1671 gold badge3 silver badges15 bronze badges asked Sep 11, 2018 at 18:25
$\endgroup$ 4 $\begingroup$ The number we seek to obtain must follow 2 conditions: a-The number must be divisible by 3 b-The number must be even You should not worry about condition (a) since a number is divisible by 3 if and only if the sum of the digits is divisible by 3, which is already obtained (1 + 3 + 4 + 6 + 7 = 21 = 3 * 7). So this condition will always be satisfied, whatever permutation you decide on. Condition (b) implies that your number must end with an even digit(Either 4 or 6). To obtain the largest number possible, you should place the smallest of these integers in the least significant positions, namely the ones. Also, intuitively, you must place the largest digits in the most significant places. So your answer would be 76314. answered Sep 11, 2018 at 18:39
$\endgroup$ $\begingroup$ The sum of the digits, 21, is divisible by 3, so any number formed from these digits is divisible by 3. So just take the digits in descending order, ensuring that the last digit is even (which I carelessly overlooked): 76314. As a check, 76431/3 =25477. answered Sep 11, 2018 at 18:34
marty cohenmarty cohen 103k9 gold badges68 silver badges167 bronze badges $\endgroup$ 2 5 digit numbers are the integers on the number line that start from 10,000 and go up to 99,999. These numbers contain a total of 5 digits in their numeric form. Let us learn more about numbers up to 5 digits in this page.
What are Numbers up to 5-Digits?Five-digit numbers start from ten thousand and extend up to ninety-nine thousand nine hundred and ninety-nine. These numbers contain integers at the places of ones, tens, hundreds, thousands, and ten thousands. Any positive integer can be placed at these places, keeping in mind that 0 cannot be placed on the ten thousands place. This is because if 0 is placed here it will become a 4-digit number, like, 04356 becomes 4356. The following figure shows how a random 5-digit number, 86953 is placed on an abacus. The place value of the five digits that make up the 5-digit number would be obtained by progressively multiplying the respective figure by 1, 10, 100, 1,000, and 10,000 starting from the rightmost digit and moving to the left. Smallest 5 Digit NumberThe smallest 5-digit number is 10,000 because 5-digit numbers start from 10,000 and the number before 10,000 is 9999 which is a 4-digit number. Greatest 5 Digit NumberThe greatest 5-digit number is 99,999 because the number after 99,999 is 1,00,000 which becomes a 6-digit number. Place Values of Digits in Numbers up to 5-DigitsAs shown above, in a 5-digit number, every progressive place value is the earlier place value multiplied by 10. For example, let us take a number: 37,159. This number can be represented in words, as, 'thirty-seven thousand one hundred and fifty-nine'. The following figure shows the place values of this 5-digit number. How to Decompose 5-Digit Numbers?When we see a 5-digit number, the five digits will correspond to the 5 place values - Units, Tens, Hundreds, Thousands and Ten Thousands. Let us see how a 5-digit number can be decomposed into its place values. Let us continue with the same number 20340. 2 is in Ten Thousands place = 2 × 10000 = 20000. Here, 0 is in Thousands place = 0 × 1000 = 0, and 3 is in Hundreds place = 3 × 100 = 300, 4 is in Tens place = 4 × 10 = 40, and 0 is in Units place = 0 × 1 = 0. Hence, the five-digit number can be expressed in the following way: 20000 + 0 + 300 + 40 + 0 = 20340. Now, how would the 5 place values change if we interchanged some of the digits? Let us change the number 20,340 to another 5-digit number having the same numbers with interchanged digits, like, 32,004. The change in place value of the same 5 digits shows the following results:
In both the numbers given above, all the zero digits have zero place value. Commas in 5-Digit NumbersWe saw the use of commas in four-digit numbers, and the position of the comma is just before the digit on the hundreds place, that is, to the left of the hundreds place. In a 5-digit number too, only one comma is to be used, and it is to be placed to the left of the hundreds place. For example, the 5-digit numbers 32958 and 20340 can be better expressed as 32,958 and 20,340 which helps in reading the numbers correctly. How Many 5-Digit Numbers Can Be Formed?As we said earlier, 02340 is not a five-digit number but a four-digit number 2340. A five-digit number cannot have 0 as the first digit on the left, which is the ten thousand place. Overall, every one of the 5 places of a 5-digit number can be filled up in ten ways, because it can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So each of the five places can be similarly filled up in ten ways. Therefore, the total number of combinations possible are 10 × 10 × 10 × 10 × 10 = 1,00,000. Out of these 1,00,000 ways of forming a 5-digit number, we need to take out all the possibilities which have zero in the first position on the left (or the ten thousand place). When there is zero in the first place, the next position (Thousands) can be filled up in ten ways, as can the Hundreds, Tens, and Units places. So, the number of 5-digit numbers that have zero as the first digit are 10 × 10 × 10 × 10 = 10,000. If we subtract these 10,000 ways from the overall 1,00,000 ways, we are left with 90,000. Therefore, there are 90,000 unique 5-digit numbers possible. Important Notes on Numbers up to 5-DigitsHere is a list of some important notes related to numbers up to 5 digits. These are helpful while we solve questions related to this topic.
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FAQs on Numbers up to 5-DigitsWhat are 5-Digit Numbers?A 5-digit number is a number that has 5 digits, in which the first digit should be 1 or greater than 1 and the rest of the digits can be any number between 0-9. It starts from ten thousand (10,000) and goes up to ninety-nine thousand, nine hundred and ninety-nine (99,999). How Many 5-Digit Numbers are there?There are 90,000 five-digit numbers including the smallest five-digit number which is 10,000 and the largest five-digit number which is 99,999. How do you Read a 5-Digit Number?We read a 5 digit number from left to write, starting from the ten thousands place to the units place. For example, the number 21,356 is read from left to right, starting from 2, followed by 1, 3, 5, and then 6. In number names, it is read as twenty-one thousand, three hundred fifty-six. How do you Write 5-Digit Numbers in Words?We write the number name of a five-digit number just the way we read it. Starting from left to right, from the ten thousands place to the units place. For example, the number 31,279 is written as thirty-one thousand, two hundred seventy-nine. What is the Smallest 5-Digit Number?The smallest five-digit number is 10,000. It is read as ten thousand in number names. What is the Largest 5-Digit Number?The largest five-digit number is 99,999 and it is written as ninety-nine thousand, nine hundred ninety-nine, in words. What is the Sum of the Greatest and the Smallest 5-Digit Numbers?The greatest 5-digit number is 99,999 and the smallest 5-digit number is 10,000. Their sum is 99,999 + 10,000=1,09,999. Which is the Greatest 5 digit number which is a Perfect Square?The greatest 5 digit number which is a perfect square is 99856. This is the square of 316 which means 3162 = 99856. What is the Successor of the Greatest 5 Digit Number?The greatest 5 digit number is 99,999. The successor of 99,999 is 1,00,000 which is read as one lakh as per the Indian place value chart and is read as a hundred thousand (100,000) as per in International place value chart. Which is the greatest 5 digit odd number?Since there are 5 unique odd digits (1 3 5 7 9), the largest 5 digit number is formed by using these 5 digits from high to low, without repeating a digit is 97531. 97,531 would be the largest digit when no number can be repeated.
What is the largest 5 digit even number without repeating digits?The largest five digit number that can be formed by the given digits without repetition of digits is 98754. However, since there is no limit on the repetition of digits, the largest number that can be formed will be 99999.
What is the greatest even digit?The greatest even number is 8 so we place 8 in the one place, in the tens place we place 9 and in hundred places we place 9.
What is the 5 digit even number?Therefore, the smallest five digit even number is 10000. So, the correct answer is “10000”.
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