Using Euclid’s Division Lemma to find HCF(865, 255)

Euclid’s Division Lemma is a method used to find the Highest Common Factor (HCF) of two numbers. Let's use this method to find the HCF of 865 and 255.

Step 1: Divide the larger number by the smaller number.

In this case, 865 is the larger number, and 255 is the smaller number.

865 ÷ 255 = 3 remainder 100

Step 2: Divide the divisor (255) by the remainder (100).

255 ÷ 100 = 2 remainder 55

Step 3: Divide the previous remainder (100) by the new remainder (55).

100 ÷ 55 = 1 remainder 45

Step 4: Repeat step 3 until the remainder is zero.

55 ÷ 45 = 1 remainder 10

45 ÷ 10 = 4 remainder 5

10 ÷ 5 = 2 remainder 0

Step 5: The HCF is the last non-zero remainder, which in this case is 5.

Therefore, the HCF of 865 and 255 is 5.

Final thoughts: Euclid’s Division Lemma is a simple and effective method for finding the HCF of two numbers. By dividing the larger number by the smaller number and then dividing the divisor by the remainder, you can quickly find the HCF. This method works for any two numbers, and it can be repeated until the remainder is zero.