The division method, also known as Euclid's Algorithm, is an efficient way to calculate the Highest Common Factor (HCF) of two or more numbers. Here are the steps:
- Divide the larger number by the smaller number. Let's say you want to find the HCF of two numbers, 'a' and 'b', where 'a > b'. Divide 'a' by 'b'.
- Find the remainder. Note down the remainder from the division in step 1.
- Replace the larger number with the smaller number and the smaller number with the remainder. So, 'a' is replaced by 'b' and 'b' is replaced by the remainder from the previous division.
- Repeat steps 1-3 until the remainder is 0. Keep dividing the previous divisor by the remainder until you get a remainder of 0.
- The last non-zero divisor is the HCF. The last divisor that gave a remainder of 0 is your HCF.
Example:
Let's find the HCF of 48 and 18:
- Divide 48 by 18: 48 ÷ 18 = 2 (quotient) with a remainder of 12.
- Now, divide 18 by 12: 18 ÷ 12 = 1 (quotient) with a remainder of 6.
- Next, divide 12 by 6: 12 ÷ 6 = 2 (quotient) with a remainder of 0.
Since the remainder is now 0, the last non-zero divisor, which is 6, is the HCF of 48 and 18.
For more than two numbers:
To find the HCF of more than two numbers, find the HCF of the first two numbers. Then, find the HCF of that result and the next number, and so on. For example, to find the HCF of 48, 18, and 30:
- We already found the HCF of 48 and 18 is 6.
- Now find the HCF of 6 and 30. Divide 30 by 6: 30 ÷ 6 = 5 (quotient) with a remainder of 0.
- Therefore, the HCF of 6 and 30 is 6.
So, the HCF of 48, 18, and 30 is 6.
