Introduction:
The division algorithm method, also known as the long division method, is a mathematical technique used to find the highest common factor (HCF) of two numbers. In this case, we will use the division algorithm method to find the HCF of 125 and 225.

Step 1: Divide and Remainder
To begin, we divide the larger number (225) by the smaller number (125) and find the remainder.

225 ÷ 125 = 1 remainder 100

Step 2: New Division
Next, we take the divisor (125) and divide it by the remainder (100) obtained in the previous step.

125 ÷ 100 = 1 remainder 25

Step 3: Continue Division
We repeat the division process using the previous divisor (100) and the new remainder (25).

100 ÷ 25 = 4 remainder 0

Step 4: Zero Remainder
Since we obtained a remainder of 0 in the previous step, we stop the division process. The divisor at this point (25) is the highest common factor (HCF) of the given numbers.

Conclusion:
Using the division algorithm method, we found that the HCF of 125 and 225 is 25.