write down the steps for finding HCF
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Answer:
Highest Common Factor (HCF)
The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. It is also known as GCD (Greatest Common Divisor).
For example, HCF of 4, 6 and 8 is 2.
HCF By Prime Factorization Method
Given natural numbers to be written as the product of prime factors. To obtain the highest common factor multiply all the common prime factors with the lowest degree (power).
Example 1:
Find the HCF of 20 and 12 by prime factorization method.
Solution:
Step 1: To find HCF of 20 and 12, write each number as a product of prime factors.
20 = 2 × 2 × 5 = 22 × 5
12 = 2 × 2 × 3 = 22 × 3
Step 2: Multiply all the common prime factors with the lowest degree.
Here we have only 2 as a common prime factor with the lowest power of 2.
HCF of 20 and 12 = 22 = 4
HCF by Division Method
In this method divide the largest number by the smallest number among the given numbers until the remainder is zero. The last divisor will be the HCF of given numbers.
Example 2:
Find the LCM of 24 and 15 by the division method.
Solution:
Step 1: Divide the largest number by the smallest number.
Here, the largest number is 24 and the smaller one is 15. Divide 24 by 15

Step 2: Take divisor as new dividend and remainder as the new divisor, i.e. divide the first divisor by the first remainder.

Step 3: Proceed till the remainder is zero and the last divisor will be the HCF of the given numbers.

Therefore, HCF of 24 and 15 is 3.
Alternatively, we can divide both the numbers by the least common prime factor, still there is no more common prime factors. Multiply all divisors to get the HCF of given numbers.
Consider the above example, HCF of 24 and 15 can also be calculated using the following steps:
Step 1: Divide the given numbers by the least common prime factor.
Here, 3 is the least common prime factor of 24 and 15.

Step 2: Continue still there is no more common prime factor. Then multiply all the divisors.
Division of 24 and 15 by 3 will leave 8 and 5 as their remainders respectively. 8 and 5 do not have a common prime factor.
Hence, the HCF of 24 and 15 is 3.
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