Find square root of 15376 by prime factorisation method.
Answers
Step-by-step explanation:
Finding the prime factors of 15,376
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.
If it doesn't make sense yet, let's try it...
Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 15,376 by 2
15,376 ÷ 2 = 7,688 - No remainder! 2 is one of the factors!
7,688 ÷ 2 = 3,844 - No remainder! 2 is one of the factors!
3,844 ÷ 2 = 1,922 - No remainder! 2 is one of the factors!
1,922 ÷ 2 = 961 - No remainder! 2 is one of the factors!
961 ÷ 2 = 480.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
961 ÷ 3 = 320.3333 - This has a remainder. 3 is not a factor.
961 ÷ 5 = 192.2 - This has a remainder. 5 is not a factor.
961 ÷ 7 = 137.2857 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
961 ÷ 31 = 31 - No remainder! 31 is one of the factors!
31 ÷ 31 = 1 - No remainder! 31 is one of the factors!
The orange divisor(s) above are the prime factors of the number 15,376. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 31 x 31 = 15,376. It can also be written in exponential form as 24 x 312.
Factor Tree
Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 15,376.
15,376
Factor Arrows
2 7,688
Factor Arrows
2 3,844
Factor Arrows
2 1,922
Factor Arrows
2 961
Factor Arrows
31 31
More Prime Factorization Examples
15,374 15,375 15,377 15,378
21 x 7,6871 31 x 53 x 411 15,3771 21 x 31 x 111 x 2331
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Answer:
The Answer is in the above Attachment.
