Question

Find the largest positive number that will divide 430 and 398 leaving a remainder 5 and 8 respectively.

Answer 1

follow these steps:

subtract remainder from corresponding numbers

n1 = 430-5 = 425

n2 = 398 - 8 = 390

now find HCF of both number  

using factor method  

factors of 425 =  5 x 5 x 17

factors of 390 = 2 x 3 x 5 x 17

common factors are 5, 17

so hcf is = 5 x 17 =  85

so answer is 85

Answer 2

Given :-

398 , 436 and 542

To Find :-

The largest number

Solution :-

Let’s assume the integer is x

According to the condition given in the question

⇒ xy+7 = 398

⇒  xz+11 = 436

⇒  xk+15 = 542

⇒ xy =391

⇒  xz = 425

⇒  xk = 527

⇒  17 × 23 = 391

⇒  17 × 25 = 425

⇒ 17 × 31 = 527

So, the largest possible integer that will divide 398,436,542 & leaves reminder 7,11 and 15 respectively was 17.