Question

find the largest possible positive integer that divides 125,162 and 259 leaving remainder 5,6 and 7 respectively.

Answer 1

Answer:

4

Step-by-step explanation:

As the remainders are 5 , 6 , 7

we are supposed to subtract the remainders from th respective numbers

so ,

125 - 5 , 162 - 6 , 259 - 7

= 120 , 156 , 252

now the numbers is divisible by a common number that is hcf

take hcf

So the hcf will turn to be 4

hence 4 will leave remainder as 5 , 6 ,7 for 125 , 162 , 259 respectively

hope u got it

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Answer 2

Answer:

12

Step-by-step explanation:

On dividing 125 by the required number, there is a remainder of 5.

That means, 125 - 5 = 120 is exactly divisible by the required number.

Similarly, 162 - 6 = 156 and 259 - 7 = 252 are divisible by required number.

So, the required number will be the HCF of 120, 156 and 252 and it can be found by using Euclid's division algorithm.

HCF of 120,156 and 252 is as follows:

156 = 120 * 1 + 36

120 = 36 * 3 + 12

36 = 12 * 3 + 0

Therefore, the largest possible positive integer is 12.

Hope it helps!