Question

If the H.C.F of 51 and 289 is expressible in the form 51m-289. Then find the value of m .​

Answer 1

Answer:

Below detailed show work will make you learn how to find HCF of 289,51 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(289,51).

Here 289 is greater than 51

Now, consider the largest number as 'a' from the given number ie., 289 and 51 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 289 > 51, we apply the division lemma to 289 and 51, to get

289 = 51 x 5 + 34

Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 34 and 51, to get

51 = 34 x 1 + 17

Step 3: We consider the new divisor 34 and the new remainder 17, and apply the division lemma to get

34 = 17 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 289 and 51 is 17

Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(289,51) .