Use Euclid’s division algorithm to find the HCF of 210 and 55.

To find the HCF of 210 and 55 using Euclid’s division algorithm, we will apply the division algorithm repeatedly until the remainder is zero. The HCF is the divisor when the remainder becomes zero.

Step 1: Divide 210 by 55

We begin by dividing 210 by 55.

210 ÷ 55 = 3 with a remainder of 45.

So, we can express this as:

210 = 55 × 3 + 45

Step 2: Divide 55 by 45

Next, we divide 55 by 45.

55 ÷ 45 = 1 with a remainder of 10.

So, we can express this as:

55 = 45 × 1 + 10

Step 3: Divide 45 by 10

Now, we divide 45 by 10.

45 ÷ 10 = 4 with a remainder of 5.

So, we can express this as:

45 = 10 × 4 + 5

Step 4: Divide 10 by 5

Next, we divide 10 by 5.

10 ÷ 5 = 2 with a remainder of 0.

So, we can express this as:

10 = 5 × 2 + 0

Since the remainder is now 0, the divisor at this step is 5, which is the HCF.

Therefore, the HCF of 210 and 55 is 5.