Question

If the Highest Common Factor of 210 and 55 is expressible in the form 55x -325 , find x​

Answer 1

Answer:

Let us first find the HCF of 210 and 55.

Applying Euclid's division lemma on 210 and 55, we get:

210 = 55 × 3 + 45 _____(i)

Since, the remainder 45 ≠ 0. So, we now apply division lemma on the divisor 55 and the remainder 45 to get:

55 = 45 × 1 + 10 _____(ii)

We consider the divisor 45 and the remainder 10 and apply division lemma to get:

45 = 4 × 10 + 5 _____(iii)

We consider the divisor 10 and remainder 5 and apply division lemma to get:

10 = 5 × 2 + 0 ______(iv)

We observe that the remainder at this stage is zero. So, the last divisor i.e. 5 is the HCF of 210 and 55.

Hence, 5 = 210 × 5 + 55y

55y = 5 - 210 × 5 = 5 - 1050

55y = - 1045

y = -1045/55

y = -19

Answer 2

Explanation:

So

55x -325 = 5

55x=330

x=6