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Find the greatest number which divides 203 and 434, leaving a remainder of 5 in each case.

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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.
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