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Find the prime factorization of 147.

A. [tex]3 \times 7 \times 7[/tex]

B. [tex]147 \times 1[/tex]

C. [tex]49 \times 3[/tex]

D. [tex]21 \times 7[/tex]

Answer :

Answer:

[tex]\textsf{A.}\;\; 3 \times 7 \times 7[/tex]

Step-by-step explanation:

Prime factorization is the process of expressing a natural number as the product of its prime factors.

To find the prime factors of a number, we divide the number successively by prime numbers, starting from the smallest prime number, until we reach 1.

Prime factorization of 147

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, ...

We cannot divide 147 by the smallest prime number, 2, since 147 is not even. Therefore, we move on to dividing by the next prime number, 3:

[tex]147 \div 3 = 49[/tex]

Since 49 is not divisible by the prime numbers 3 or 5, we move on to dividing it by the next prime number which is 7:

[tex]49 \div 7 = 7[/tex]

Finally, we divide 7 by 7:

[tex]7 \div 7 = 1[/tex]

The number of times we divide by a prime number determines how many times it appears in the prime factorization. Since we divided by 3 once and by 7 twice, the prime factorization of 147 is:

[tex]147 = \boxed{3 \times 7 \times 7}[/tex]

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