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Primary 1 | Maths
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It means that 15 is smaller than this largest number. (thus leaving a remainder, otherwise it would be divisible and there would be no remainder!)
So the number is larger than 15.
398 - 7 = 391
436 - 11 = 425
542 - 15 = 527
391, 425 and 527 can be divided by this number.
We can choose 2 numbers from the 3 and find their difference. The smallest difference could be that largest number, or could be divisible by it.
There are 3 possible cases.
Case 1 : 425 and 391
Difference = 425 - 391 = 34
Case 2 : 527 and 425
Difference = 527 - 425 = 102
Case 3 :
Difference = 527 - 391 = 136
As 34 is the smallest difference between two numbers, we should try to divide the numbers by 34 to see if there is a remainder.
However, notice that the numbers 391,425 and 527 are odd.
The product of an odd whole number and an even whole number is always an even whole number.
The product of an odd whole number and another odd whole number is always an odd whole number.
So, if we try to divide the odd whole numbers by 34(which is an even whole number) , we will definitely not get a whole number , and there will definitely be a remainder.
So let's divide 34 by some even whole number to make it odd, in order to get a whole number.
We divide it by the smallest even whole number, 2, since we want the number to be as large as possible (question asked for largest number)
34 ÷ 2 = 17
So the largest number is 17.
Check :
391 ÷ 17 = 23 (divisible)
425 ÷ 17 = 25 (divisible)
527 ÷ 17 = 31 (divisible)
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