Question

By using Euclid’s division algorithm, find the largest number which when divides 969 and 2059, gives the remainders 9 and 11, respectively.

Answer 1

In order to find the largest number which divides 969 and 2059 and leaves remainders 9 and 11, respectively, we've to find the HCF of :-

• 969 - 9 = 960
• 2059 - 11 = 2048

$= > 960 = {2}^{6} \times 3 \times 5 \\ \\ = > 2048 = {2}^{11}$

Here, H.C.F of 960 and 2048 is :-

2 × 2 × 2 × 2 × 2 × 2

= 64

Therefore,

64 is the largest number that divides 969 and 2059, leaving the remainders 9 and 11 respectively.

$\rule{200}2$

Answer 2

Answer:

64 is answer dear friend