To find the greatest number which divides 203 and 434 leaving a remainder of 5 in each case, follow these steps:
1. Understand the problem:
We need to determine the largest number that divides both 203 and 434, such that each division leaves a remainder of 5.
2. Subtract the remainder:
Since dividing the numbers 203 and 434 by the unknown number leaves a remainder of 5, we first subtract 5 from each number.
[tex]\( 203 - 5 = 198 \)[/tex]
[tex]\( 434 - 5 = 429 \)[/tex]
3. Identify the numbers to work with:
Now, we need to find the greatest common divisor (GCD) of the numbers 198 and 429.
4. Find the GCD of 198 and 429:
When we calculate the GCD of 198 and 429, we find that it is 33.
So, the greatest number that divides both 203 and 434 and leaves a remainder of 5 in each case is 33.
