When 31513 and 34369 are divided by a certain three digit no. the remainder are equal. Find this remainder.
To find the remainder when two numbers are divided by a certain number, we need to use the concept of modular arithmetic.
In this case, we have two numbers: 31513 and 34369, and we want to find a three-digit number that gives the same remainder when dividing both numbers.
Let's denote the three-digit number as "x". To find the remainder when dividing 31513 by x, we can use the modulo operation: 31513 % x. Similarly, to find the remainder when dividing 34369 by x, we can use the same modulo operation: 34369 % x.
Since the problem states that the remainders are equal, we have the equation: 31513 % x = 34369 % x.
To find the value of x, we can calculate the remainders for different possible three-digit numbers and check which one satisfies the equation. We do this iteratively until we find a number that works.
Here's an example of how we can approach this problem:
1. Start with a three-digit number x = 100.
2. Calculate the remainders for both numbers: remainder1 = 31513 % 100 and remainder2 = 34369 % 100.
3. Check if the remainders are equal: if remainder1 == remainder2, then we have found a potential value for x. If not, we increment x by 1 and repeat steps 2 and 3.
4. Continue this process until we find a value for x that satisfies the equation.
Using this approach, we can find the remainder when dividing 31513 and 34369 by a certain three-digit number.
34369 - 31513 = 2856
Then we list all divisors of 2856:
1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 51, 56, 68, 84, 102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952, 1428, 2856
From here, we take all the 3-digit numbers:
102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952
There are 11 possible answers.
Hope this helps.