Question

four students tried to create a factor table for the number 83. complete the statements below about the number 83. table a: factors of 83 1 | 83 table b: factors of 83 1 | 83 7 | 13 table c: factors of 83 1 | 83 13 | 70 27 | 56 table d: factors of 83 1 | 83 3 | 21 7 | 9 the factor table that correctly shows the factors of 83 is dropdown. the number 83 has dropdown factors. the number 83 is a dropdown number.

Explanation:

Step1: Recall factor definition

A factor of a number \( n \) is an integer that divides \( n \) without a remainder. For 83, we check which pairs multiply to 83.

Step2: Analyze Table A

Table A has 1 and 83. \( 1 \times 83 = 83 \), so these are factors.

Step3: Analyze Table B

Check \( 7 \times 13 = 91
eq 83 \), so invalid.

Step4: Analyze Table C

\( 13 \times 70 = 910
eq 83 \), \( 27 \times 56 = 1512
eq 83 \), invalid.

Step5: Analyze Table D

\( 3 \times 21 = 63
eq 83 \), \( 7 \times 9 = 63
eq 83 \), invalid.

Step6: Determine number of factors

Since only 1 and 83 are factors, 83 has 2 factors.

Step7: Classify 83

A prime number has exactly 2 distinct positive factors (1 and itself), so 83 is prime.

Answer:

The factor table that correctly shows the factors of 83 is Table A.
The number 83 has 2 factors.
The number 83 is a prime number.