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Prime Factorisation Method to find HCF
To find the highest common factor (HCF) of a set of numbers, we can use the prime factorisation method. This method involves finding the prime factors of each number and then determining the common factors.
Let's solve the given example using the prime factorisation method.
Example
Find the HCF of the following numbers: 12, 18, 24
Solution
Step 1: Prime Factorisation of each number
To find the prime factors of each number, we divide them by prime numbers until we can no longer divide evenly.
For 12:
12 ÷ 2 = 6
6 ÷ 2 = 3
So, the prime factors of 12 are 2 and 3.
For 18:
18 ÷ 2 = 9
9 ÷ 3 = 3
So, the prime factors of 18 are 2 and 3.
For 24:
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
So, the prime factors of 24 are 2 and 3.
Step 2: Identify the common factors
To find the HCF, we need to determine the common factors among the prime factors of the given numbers.
In this case, the common factors are 2 and 3.
Step 3: Multiply the common factors
To find the HCF, we multiply the common factors together.
HCF = 2 × 3 = 6
Therefore, the HCF of the numbers 12, 18, and 24 is 6.
Summary
Using the prime factorisation method, we found that the HCF of the numbers 12, 18, and 24 is 6. This method involves finding the prime factors of each number and then identifying the common factors. Finally, we multiply the common factors to find the HCF.
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