How To Find The Square Root Of A Number By Prime Factor Method

In one of my previous articles, I had discussed the ways of finding the square root of any perfect square root by the division method. There is another way of finding the square root of any perfect square. This second method is called the prime factors method. As the title suggests, the numbers deal with prime factors only.
As an example, let us find the square root of 7744. (For your information, the square root of 7744 is 88.)
7744 is divisible by 2. So the first step will be dividing 7744 by 2. This quotient is 3872. The

first step will be 7744 = 2 X 3872. As 3872 is not a composite number, it is divisible by 2. This quotient will be 1936. This forms the second step as follows: 7744 = 2 X 2 X 1936. 1936 is also divisible by 2. The quotient is 968. Similarly, keep on dividing each new quotient by 2 as long as you cannot
divide by 2.
You will finally reach 121 as one of the quotients. Now, the number 121 is not divisible by 2. So, you have to move on to the next prime number, which is 3. You will notice that even 121 is not divisible by 3 or 7. But the next prime number – 11 can perfectly divide 121. The last two factors in the series will be 11 X 11.
This is how you will get a final look of all the steps of the prime factors of 7744.
7744 = 2 X 3872
= 2 X 2 X 1936
= 2 X 2 X 2 X 968
= 2 X 2 X 2 X 2 X 484
= 2 X 2 X 2 X 2 X 2 X 242
= 2 X 2 X 2 X 2 X 2 X 2 X 121
= 2 X 2 X 2 X 2 X 2 X 2 X 11 X 11
Now, form two pairs of each factor starting from the left to the right. The number 2 appears six times in all. This means there will be three pairs of 2s. The pair of 11 appears only once as shown above. Get each factor from one pair to get their product. This will be as follows: 2 X 2 X 2 X 11 = 88.
The product 88 is the square root of 7744.

Article Written By abhi_bangal

I am a professional writer and also run a couple of sites on technology and blogging.

Last updated on 30-07-2016 7K 0

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