Question

factor pairs of 17
1 | 17
2 | not a factor
3 | not a factor
4 | not a factor
5 | not a factor

the number 17 has ? factors.

the number 17 is a prime / composite number.

Explanation:

Step1: Recall factor definition

A factor of a number \( n \) is an integer that divides \( n \) without leaving a remainder. For 17, we check divisibility by integers starting from 1.

Step2: Check divisors of 17

• \( 17\div1 = 17 \), so 1 and 17 are factors.
• \( 17\div2 = 8.5 \) (not an integer, so 2 is not a factor).
• \( 17\div3\approx5.67 \) (not an integer, so 3 is not a factor).
• \( 17\div4 = 4.25 \) (not an integer, so 4 is not a factor).
• \( 17\div5 = 3.4 \) (not an integer, so 5 is not a factor).
• Continuing, we see only 1 and 17 divide 17 without remainder. So the number of factors is 2.

Step3: Define prime/composite

A prime number has exactly 2 distinct positive factors (1 and itself), and a composite number has more than 2 factors. Since 17 has 2 factors, it is prime.

Answer:

The number 17 has \(\boldsymbol{2}\) factors. The number 17 is a \(\boldsymbol{prime}\) number.