Question

prime factorization
write the factors on each branch to complete a prime factor tree.
example
20
5 4
2 2
20 = 2 x 2 x 5
1
63
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63 = x x
4
99
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99 = x x
2
27
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27 = x x
5
110
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110 = x x
3
154
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154 = x x
6
165
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165 = x x

Explanation:

Problem 1: Prime Factorization of 63

Step1: Find two factors of 63

We know that \( 63 = 7 \times 9 \). Here, 7 is a prime number, and 9 is a composite number.

Step2: Factorize 9

Factorize 9 further: \( 9 = 3 \times 3 \), and both 3s are prime numbers.

Step3: Write the prime factors

So, the prime factorization of 63 is \( 63 = 7 \times 3 \times 3 \).

Step1: Find two factors of 27

We have \( 27 = 3 \times 9 \). 3 is a prime number, and 9 is composite.

Step2: Factorize 9

Factorize 9: \( 9 = 3 \times 3 \), both 3s are prime.

Step3: Write the prime factors

Thus, the prime factorization of 27 is \( 27 = 3 \times 3 \times 3 \).

Step1: Find two factors of 154

We get \( 154 = 2 \times 77 \). 2 is a prime number, and 77 is composite.

Step2: Factorize 77

Factorize 77: \( 77 = 7 \times 11 \), both 7 and 11 are prime numbers.

Step3: Write the prime factors

So, the prime factorization of 154 is \( 154 = 2 \times 7 \times 11 \).

Answer:

\( 63 = 7 \times 3 \times 3 \)

Problem 2: Prime Factorization of 27