Question

The greatest number which will divide both 584 and 134 to leave a reminder as 8 in each case

Answer 1

Let the greatest number be x.

Let 584 = px + 8.    →   (1)

And let 134 = qx + 8.    →   (2)

So that both px + 8 and qx + 8 leave remainder 8 on division by x.

(1) + (2)

(px + 8) + (qx + 8) = 584 + 134

px + qx + 16 = 718

px + qx = 718 - 16

px + qx = 702    →   (3)

(1) - (2)

(px + 8) - (qx + 8) = 584 - 134

px + 8 - qx - 8 = 450

px - qx = 450    →   (4)

(3) + (4)

(px + qx) + (px - qx) = 702 + 450

2px = 1152

px = 576

(3) - (4)

(px + qx) - (px - qx) = 702 - 450

2qx = 252

qx = 126

So the answer is the HCF of px and qx.

Find the HCF of 576 and 126.

HCF = 18

   

∴ 18 is the answer.

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But there's no need for such a huge method to find the answer.

Here, the remainder is 8. So subtract 8 each from 584 and 134, and then find the HCF of the numbers obtained to get the answer. That's all!!! But I got it now!!! ;-b

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Hope this may be helpful.

Thank you. Have a nice day. :-))

#adithyasajeevan