Question

Find the largest number that divides 628,3129 and 15630 to leave reminders 3,4 and 5 respectively.

Answer 1

Required number
= HCF of (628 3), (3129 -4) and (15630 5) i.e., required number
= HCF of 625, 3125, 15625

To find HCF of 625, 3125 and 15625 first we will find HCF of 625 and 3125 and then we will find HCF of HCF of (625 & 3125) and 15625.

Step (1) : HCF of 625 and 3125 by using Euclid’s division algorithm is 3125 =625x5+0
=:> HCF of 625 and 3125 is 625.

Step (2): Now HCF of 625 and 15625 will be : 15625 = 625 x 25 + O
=:> HCF of 625 and 15625 is 625. . Hence HCF of 625, 3125 and 15625 is 625. Hence, required number is 625.