The successive division method, also known as the continued division method, is a technique used to find the Highest Common Factor (HCF) of two numbers. Here's how it works:
-
Divide: Divide the larger number by the smaller number.
- For example, if you want to find the HCF of 85 and 34, divide 85 by 34. The reference exemplifies this: "So here we divide eighty-five by thirty-four".
-
Find the Remainder: Determine the remainder of the division.
- Continuing the example, 85 divided by 34 gives a quotient of 2 and a remainder of 17 because "34 into 2 is equal to 68...subtract 68 from 85 to get the remainder 17."
-
New Division: If the remainder is not zero, make the remainder the new divisor and the previous divisor the new dividend. Divide the previous divisor by the remainder.
- In our example, the remainder 17 becomes the divisor, and the previous divisor, 34, becomes the new dividend.
-
Repeat: Continue this process of dividing the previous divisor by the remainder until you get a remainder of zero.
-
HCF: The last non-zero divisor is the HCF of the original two numbers.
Let's illustrate this with the example of finding the HCF of 85 and 34, based on the reference:
| Division | Dividend | Divisor | Quotient | Remainder |
|---|---|---|---|---|
| First Division | 85 | 34 | 2 | 17 |
| Second Division | 34 | 17 | 2 | 0 |
Since the remainder is now 0, the last non-zero divisor, which is 17, is the HCF of 85 and 34.
Therefore, HCF (85, 34) = 17.
