What is the largest number that divides 245 and 1029 , leaving 5 as remainder in each case.
Question
Solution
To find the largest number that divides 245 and 1029, leaving a remainder of 5 in each case, we need to find the greatest common divisor (GCD) of (245-5) and (1029-5).
Step 1: Subtract 5 from each number. 245 - 5 = 240 1029 - 5 = 1024
Step 2: Find the GCD of 240 and 1024.
The GCD of 240 and 1024 is 16.
So, the largest number that divides 245 and 1029, leaving a remainder of 5 in each case, is 16.
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