Question

Write the prime factorizations of 16, 28, and 38.

Answer 1

Hint: - Calculate the factors of the numbers and convert them into multiplication of prime numbers.

We have to find out the prime factorizations of 16, 28, and 38.
So, factorize these numbers
Therefore 16 factorization \[{\text{ = 2}} \times 2 \times 2 \times 2\], (2 is a prime number)
A number is called a prime number if the factor of the number is either 1 or itself.
So, 2 is multiplied four times to make the original number.
28 factorization \[{\text{ = 2}} \times 2 \times 7\], (2 and 7 are prime number)
So, 2 is multiplied two times and 7 is multiplied one time together to make the original number.
38 factorization \[{\text{ = 2}} \times 19\], (2 and 19 are prime number)
So, 2 is multiplied one time and 19 is multiplied one time together to make the original number.
$\therefore $Prime factorization of 16\[ = {2^4}\]
$\therefore $Prime factorization of 28\[ = {2^2} \times 7\]
$\therefore $Prime factorization of 38\[ = {\text{2}} \times 19\]

Note: - In such types of questions the key concept we have to remember is that prime factorization is finding which prime number multiplies together to make the original number, so calculate the factors of the numbers and convert them into multiplication of prime numbers, which is the required prime factorization.