How is HCF method done ? Please explain me
Answers
Answer:
The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.
Explanation:
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ANSWER:
HCF
HCF stands for highest common factor. It is also known as greatest common divisor or GCD. Let us consider a1 and a2 as the two natural numbers. If these two natural numbers a1 and a2 are divisible by exactly the same number which is n then ‘n’ is called the common factor ofa1 and a2. The highest number of all these common factors ofa1 and a2 is called as the HCF or GCD. For example, the highest common factor of 18 and 24 is 6.
1. Factorization method
2. Division method
1. Factorization Method
In this method, write the numbers in the standard form. The prime numbers that are common to all the numbers and their factors will be our required HCF.
Examples
Q. Find the HCF of 160, 220, 340.
First, we will start by writing the numbers in the standard form. Thus, the numbers will be written as:
160 = 2³ x 2² x 5
220 = 2² x 5 x 11
340 = 2² x 5 x 17
So, the numbers common in the above sequence are 2² and 5. Thus, the HCF of the given numbers will be 2² x 5 = 20.
2. Division Method
For this method, take two of the given numbers, divide the greater by the smaller and then divide the divisor by the reminder. Now again divide the divisor of this division by the next remainder found and repeat this method until the remainder is zero. The last divisor that is found will be the HCF of the two numbers asked. If there are three numbers given and you need to find the HCF of three numbers then find the HCF of this two numbers and the third number.
Examples
Q. What will be the HCF of 327 and 436?
Here first we have to check which number is smaller. And we will use that small number as a divisor to divide the larger number. Here 327 is a smaller number and 436 is a larger number. So we will divide 436 by 327.
Here the remainder is 109. Now we will divide 327 by 109.
So, the HCF of 327 and 436 is 109.
Q. Find the HCF of 324, 576, and 784
The division method becomes a bit complicated when you try and find the HCF of three numbers. We will start by taking two numbers and then we will find HCF of the third number. Let’s start with 784 and 576,
576 ) 784 ( 1
-576
208 ) 576 ( 2
– 416
160 ) 208 ( 1
– 160
48 ) 160 ( 2
– 144
16 ) 48 ( 3
– 48
0
So, the HCF of 576 and 784 is 16.
Now find the HCF of 16 and the remaining number i.e. 324.
16 ) 324 ( 20
– 320
4 ) 160 ( 40
– 160
0
Thus, we have found that the HCF of 576, 784, and 324 is 4.