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

To find the Highest Common Factor (HCF) of 55 and 210 using Euclid’s division algorithm, we follow a systematic approach involving division and remainders.

Step 1: Initial Division

First, we divide the larger number (210) by the smaller number (55).

• 210 ÷ 55 = 3 (quotient)
• Remainder = 210 - (55 × 3) = 210 - 165 = 45

Step 2: Repeat the Process

Next, we take the previous divisor (55) and divide it by the remainder (45).

• 55 ÷ 45 = 1 (quotient)
• Remainder = 55 - (45 × 1) = 55 - 45 = 10

Step 3: Continue Until Remainder is Zero

Now, we divide 45 by the new remainder (10).

• 45 ÷ 10 = 4 (quotient)
• Remainder = 45 - (10 × 4) = 45 - 40 = 5

Next, we divide 10 by 5.

• 10 ÷ 5 = 2 (quotient)
• Remainder = 10 - (5 × 2) = 10 - 10 = 0

Final Result

When the remainder reaches zero, the last non-zero remainder is the HCF. Here, the last non-zero remainder is 5.

The HCF of 55 and 210 is 5.