Question

Find the HCF of 28 and 126 by prime factor method.

Answer 1

Hint: According to the question given in the question we have to find the HCF of 28 and 126 by prime factor method. So, first of all we have to understand about the prime factorization method which is explained below:
Prime factorization method: In the prime factorization method we have to start dividing the number by the first prime number which is 2 and we have to continue dividing by 2 until we get a remainder or decimal. After it we have to divide it by other prime numbers like 3, 5, 7, …………. Until the only numbers left are the prime numbers.
Now, we have to factorize the given number 28 with the prime numbers as (2, 3, 5, 7, …………….)
Now, same as we have to factorize the given number 126 with the prime numbers as (2, 3, 5, 7, …………….)
After that we can obtain the HCF of 28 and 126 by prime factor method.

Complete step-by-step answer:
Step 1: First of all we have to factorize the given number 28 with the prime numbers starting with 2 as mentioned in the solution hint. Hence,
$
   \Rightarrow 28 = 2 \times 2 \times 7 \\
   \Rightarrow 28 = {2^2} \times 7
 $
Step 2: Now, same as the step 1 we have to factorize the given number 28 with the prime numbers starting with 2 as mentioned in the solution hint. Hence,
$
   \Rightarrow 126 = 2 \times 3 \times 3 \times 7 \\
   \Rightarrow 28 = 2 \times {3^2} \times 7
 $
Step 3: Now, from the step 1 and the step 2 we can obtain the HCF of (28, 126) as given below:
\[
   \Rightarrow (28,126) = {2^1} \times {3^0} \times {7^1} \\
   \Rightarrow (28,126) = 2 \times 7 \\
   \Rightarrow (28,126) = 14
 \]

Hence, we have obtained the HCF of 28 and 126 by prime factor method which is equal to 14.

Note: To find the factor of a given number by prime factorization method it is necessary to divide the given number with the first prime number and as we know that the first prime number is 2 we will continue dividing the given number with prime number 2 until we obtain the remainder or decimal value and after that we will divide the obtain number by other prime numbers after 2 as (3, 5, 7, 11, …………………)