Question

emma has checked that 1155 is divisible by the primes 3, 5, and 7 and therefore thinks that the prime factorization of 1155 is 3 \cdot

select the correct answer below and fill in the answer box(es) to complete your choice.

a. emma has divided incorrectly. instead of 3, 5, and 7, she should have gotten 1, 5, and 7.
b. emma has included an extra term in the prime factorization. the extra term is
c. emma is missing the term in the prime factorization.
d. emma is missing the terms and in the prime factorization. (use ascending order.)

Explanation:

Find the product of the identified prime factors

We are given that Emma checked divisibility of \(1155\) by the primes \(3\), \(5\), and \(7\).
Let's compute the product of these three prime factors:

$$ 3 \times 5 \times 7 = 105 $$

Determine the missing factor

Using the Prime Factorization Divisibility concept, we divide the original number by this product to find the remaining factor:

$$ \frac{1155}{105} = 11 $$

Verify the prime factorization

Since \(11\) is also a prime number, the complete prime factorization of \(1155\) is:

$$ 1155 = 3 \times 5 \times 7 \times 11 $$

Identify the correct option

Emma thinks the prime factorization is \(3 \times 5 \times 7\).
Comparing this with the actual prime factorization \(3 \times 5 \times 7 \times 11\), she is missing the prime factor \(11\).
Therefore, option C is the correct choice, and the missing term is \(11\).

Answer:

• (A) Emma has divided incorrectly. Instead of 3, 5, and 7, she should have gotten <blank>1</blank>, <blank>5</blank>, and <blank>7</blank>.
• (B) Emma has included an extra term in the prime factorization. The extra term is <blank></blank>.
• (C) Emma is missing the term <blank>11</blank> in the prime factorization. (Correct answer)
• (D) Emma is missing the terms <blank></blank> and <blank></blank> in the prime factorization. (Use ascending order.)