Question

By using division algorithm. find the largest number which divides 969 and 2059, remainders obtained are 9 and 11​

Answer 1

$\huge{\underline{\underline{\green{\mathfrak{Answer:}}}}}$

let the number which divides 969 and 2059 be n

Since the number 969 and 2059 leaves remainder of 9 and 11 respectively

So,

(969 - 9) = 960 {multiple of n}

(2059 - 11) = 2048 {multiple of n}

Now, using Euclids division algorithm:

Let, a = 2047 and b = 960

a = bq + r, where 0 ≤ r ≤ b

=> 2048 = 960 × 2 + 128

=> 960 = 128 × 7 + 64

=> 128 = 64 × 2 + 0

=> HCF(2047, 960) = 64

So, the largest number that divides 969, 2059 and leaves 9 and 11 as remainder is 64