what is the most largest possible find digit number divisible by 12 that you can make from the digit 1 2 3 5 and one more digit
Answer (1)
Answer:Finding the Largest 5-Digit Number Divisible by 12 Using Digits 1, 2, 3, 5, and One Extra DigitImagine you have the digits 1, 2, 3, and 5, and you can add one more digit of your choice. Your goal is to create the biggest 5-digit number possible that can be divided evenly by 12.What does divisible by 12 mean?A number is divisible by 12 if:It’s divisible by 3 — which means the sum of its digits can be divided by 3 without any remainder.It’s divisible by 4 — which means the last two digits of the number form a number that can be divided by 4 without any remainder.Step 1: Pick the extra digitFirst, we need to pick the extra digit wisely so the total sum of all five digits is divisible by 3.The sum of the digits 1 + 2 + 3 + 5 = 11.We want to add a digit (let’s call it X) so that 11 + X is divisible by 3.The digits that make 11 + X divisible by 3 are 1, 4, or 7.To get the biggest number, we pick the largest digit possible: 7.Step 2: Check the digits and sumNow, our digits are 1, 2, 3, 5, and 7. Their sum is 18, which is divisible by 3 — perfect!Step 3: Arrange the digits to make the biggest number divisible by 4 at the endTo make the number as big as possible, put the biggest digits at the front. So, start with 7 and 5.But remember, the last two digits must form a number divisible by 4. Some possible last two digits from our digits are:12 (because 12 ÷ 4 = 3)32 (because 32 ÷ 4 = 8)52 (because 52 ÷ 4 = 13)72 (because 72 ÷ 4 = 18)We want to keep the biggest digits upfront, so try putting 7, 5, and 3 at the start, and 1 and 2 at the end to make "12" at the end.This gives us 75,312.Step 4: Double-checkIs 75,312 divisible by 3?Sum of digits = 7 + 5 + 3 + 1 + 2 = 18, which divides evenly by 3.Is 75,312 divisible by 4?Last two digits are 12, and 12 divides evenly by 4.So yes, 75,312 is divisible by 12!Final answer:The biggest 5-digit number you can make with digits 1, 2, 3, 5, and one extra digit that is divisible by 12 is:75,312If you want, I can help you explore other digits or numbers too!Step-by-step explanation:Step 1: Understand divisibility rules for 12Divisible by 3: Sum of digits must be divisible by 3.Divisible by 4: Last two digits form a number divisible by 4.Step 2: Sum of given digitsAdd digits 1 + 2 + 3 + 5 = 11.Step 3: Choose the extra digit (X)Find X so that (11 + X) is divisible by 3.Possible X values: 1, 4, or 7 (because 11 + 1 = 12, 11 + 4 = 15, 11 + 7 = 18, all divisible by 3).Pick the largest X to maximize the number: 7.Step 4: List all digitsDigits: 1, 2, 3, 5, 7.Sum = 18 (divisible by 3 ✅).Step 5: Arrange digits to form the largest numberStart with the largest digits at the front: 7, 5, 3, ...Last two digits must form a number divisible by 4.Step 6: Check last two digits divisible by 4Possible pairs from remaining digits: 12, 32, 52, 72.Among these, 12 is divisible by 4.Step 7: Form the numberPut 7, 5, 3 at the front, and 1, 2 at the end → 75312.Step 8: Verify divisibilitySum digits: 7 + 5 + 3 + 1 + 2 = 18 (divisible by 3).Last two digits: 12 (divisible by 4).So, 75312 is divisible by 12.Final answer:75,312 is the largest 5-digit number divisible by 12 you can make with digits 1, 2, 3, 5, and one extra digit.
