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25 Jan 2017, 23:12
Kudos
Bookmarks
For the below problem. I know how to solve it, but want to know why this approach works?
Q: find greatest number which, when it divides 69, 141, 189 leaves same remainder?
A:
Step1: Find diff of all numbers 141-69 = 72, 189-141 = 48, 189-69 = 120.
Step2: Find GCD (72, 48, 120) = 24.
ans = 24. rem(24 , 141, 189) when divided by 24 = 21.
I am not sure why this approach worked and what we are trying to do in step 1. Thought process to solve this problem is not clear. Any suggestions?
Q: find greatest number which, when it divides 69, 141, 189 leaves same remainder?
A:
Step1: Find diff of all numbers 141-69 = 72, 189-141 = 48, 189-69 = 120.
Step2: Find GCD (72, 48, 120) = 24.
ans = 24. rem(24 , 141, 189) when divided by 24 = 21.
I am not sure why this approach worked and what we are trying to do in step 1. Thought process to solve this problem is not clear. Any suggestions?
26 Jan 2017, 20:24
Kudos
Bookmarks
avinashvpec
For the below problem. I know how to solve it, but want to know why this approach works?
Q: find greatest number which, when it divides 69, 141, 189 leaves same remainder?
A:
Step1: Find diff of all numbers 141-69 = 72, 189-141 = 48, 189-69 = 120.
Step2: Find GCD (72, 48, 120) = 24.
ans = 24. rem(24 , 141, 189) when divided by 24 = 21.
I am not sure why this approach worked and what we are trying to do in step 1. Thought process to solve this problem is not clear. Any suggestions?
Q: find greatest number which, when it divides 69, 141, 189 leaves same remainder?
A:
Step1: Find diff of all numbers 141-69 = 72, 189-141 = 48, 189-69 = 120.
Step2: Find GCD (72, 48, 120) = 24.
ans = 24. rem(24 , 141, 189) when divided by 24 = 21.
I am not sure why this approach worked and what we are trying to do in step 1. Thought process to solve this problem is not clear. Any suggestions?
Hi avinashvpec,
We write down 69, 141, 189 in the following way.
69 = n * r1 + q
141 = n * r2 + q
189 = n * r3 + q
141 - 69 = 72 = n*(r2-r1)
189 - 141 = 48 = n*(r3-r2)
189 - 69 = 120 = n*(r3-r1)
n is a divisor of GCD(72,48,120) = 24.
Then n is one of 24, 12, 8, 6, 4, 3, 2, 1 and so check one by one from 24 to 1.
Since 24 genereates the same remainder 21.
Therefore, the answer is 24.
Happy Studying!
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