**Euclid's Division Algorithm**

Euclid's Division Algorithm is a method used to find the highest common factor (HCF) of two positive integers. It involves dividing the larger number by the smaller number and repeating the process until the remainder becomes zero. The HCF is then the last non-zero remainder obtained in the process.

**Given Numbers: 72, 126, 150**

Let's find the HCF of 72, 126, and 150 using Euclid's Division Algorithm.

**Step 1: Find HCF of 72 and 126**

To find the HCF of 72 and 126, we divide the larger number (126) by the smaller number (72) and find the remainder.

126 ÷ 72 = 1 remainder 54

Now, we divide the divisor (72) by the remainder (54) and find the new remainder.

72 ÷ 54 = 1 remainder 18

We repeat this process until the remainder becomes zero.

54 ÷ 18 = 3 remainder 0

Since the remainder is now zero, we stop the process. The last non-zero remainder obtained was 18. Therefore, the HCF of 72 and 126 is 18.

**Step 2: Find HCF of 18 and 150**

To find the HCF of 18 and 150, we follow the same process as in Step 1.

150 ÷ 18 = 8 remainder 6

18 ÷ 6 = 3 remainder 0

The last non-zero remainder obtained was 6. Therefore, the HCF of 18 and 150 is 6.

**Step 3: Find HCF of 6 and 0**

Since the remainder is zero in the previous step, we stop the process. The last non-zero remainder obtained was 6. Therefore, the HCF of 6 and 0 is 6.

**Final Result: HCF of 72, 126, and 150 is 6**

Therefore, the highest common factor (HCF) of 72, 126, and 150 is 6, which is obtained using Euclid's Division Algorithm.

According to Euclid's division algorithm
126 ÷72
126= 72X1 +54
72= 54X1 +18
54= 18X3 +0
therefore,HCF of126 and 72 =18

then , 150 ÷18
150 = 18X 8 + 6
18 = 6X 3 + 0

therefore total HCF of 72 ,126 and 150 = 6

Hope it helps