Question

one way to determine whether a number is prime or composite is by creating a factor table.
complete the factor table and the sentences below about the number 17.
factor pairs of 17
1 17
2 (not a factor)
3 (not a factor)
4
5
the numbers 17 (not a factor) tors.

Explanation:

Step1: Recall the definition of a factor

A factor of a number \( n \) is an integer that divides \( n \) without leaving a remainder. So we need to check which of the given options (4, 8, 13) divides 17 evenly.

Step2: Check divisibility by 4

Divide 17 by 4: \( 17\div4 = 4.25 \), which is not an integer. So 4 is not a factor.

Step3: Check divisibility by 8

Divide 17 by 8: \( 17\div8 = 2.125 \), which is not an integer. So 8 is not a factor.

Step4: Check divisibility by 13

Divide 17 by 13: \( 17\div13\approx1.307 \), which is not an integer. Wait, but we know that 17 is a prime number, and its only factor pairs are (1, 17). Wait, maybe there's a mistake in the options? Wait, no, the table is for factor pairs of 17. Wait, the first row is 1 and 17. Then for 2: 17÷2 = 8.5, not integer. For 3: 17÷3≈5.666, not integer. For 4: 17÷4 = 4.25, not integer. For 5: 17÷5 = 3.4, not integer. Wait, but the dropdown has 4, 8, 13, and "not a factor". Wait, the correct option for each of these (2,3,4,5,...) should be "not a factor" because 17 is prime. But let's check the dropdown again. Wait, maybe the question is about filling the factor table. Let's re-express:

For the row with 4: we need to see if 4 is a factor. Since 17 divided by 4 is not an integer, we choose "not a factor". Wait, but the dropdown has "not a factor" as an option? Wait, the user's image shows the dropdown with 4, 8, 13, and "not a factor". So for each number (2,3,4,5,...), we check if it's a factor. Since 17 is prime, its only factors are 1 and 17. So for 4: 17 ÷ 4 is not an integer, so we select "not a factor". Wait, but maybe I misread. Wait, the problem is to complete the factor table for 17. Let's list all numbers from 1 to, say, 17 and check which are factors.

The factors of 17 are 1 and 17 (since 17 is prime: it has only two distinct positive divisors: 1 and itself). So for the row with 4: 4 is not a factor of 17, so we select "not a factor". Wait, but the dropdown has "not a factor" as an option? Wait, the user's dropdown for 4 has options 4, 8, 13, "not a factor". So the correct choice is "not a factor" because 4 does not divide 17. Wait, but maybe the original problem was cut off, but based on the factor table, for each number (2,3,4,5,...), we check if it's a factor. Since 17 is prime, all numbers from 2 to 16 (except 17, but 17 is the number itself) are not factors. So for 4, the correct option is "not a factor".

Answer:

For the row with 4 in the factor table of 17, the correct choice is "not a factor". (Assuming the dropdown includes "not a factor" as an option; if we have to choose from 4,8,13, none are factors, but since "not a factor" is an option, that's the answer.)