Question

please answer the 2 question in example 12

Answer 1

Given that when 258 is divided by the number the remainder is 6.

 Similarly, when 584 is divided by the same number the remainder is 8. 

The largest number which divides (258 – 6) and
(584 – 8) is their HCF.

HCF of 252 and 576 (by Euclid division algorithm)
576 = 252 × 2 + 72
252 = 72 × 3 + 36 
72 = 36 × 2 + 0 

Hence the HCF of 252 and 576 is 36. 

Thus the largest number that divides 258 and 584 leaving remainder 6 and 8 respectively is 36.