Question

two numbers multiplied together are both factors of the resulting number. which two numbers are factors of 30? 0 and -30; -1 and -25; -2 and -17; -3 and -10

Explanation:

Step1: Recall factor definition

A factor of a number \( n \) is an integer that divides \( n \) without leaving a remainder. Also, if \( a \) and \( b \) are factors of \( n \), then \( a\times b = n \) (or \( a\times b \) is a multiple of \( n \), but here we check if their product is \( 30 \) and they divide \( 30 \)).

Step2: Check Option 1 (0 and -30)

Multiply: \( 0\times(-30)=0
eq30 \). Also, \( 0 \) is not a factor (since division by \( 0 \) is undefined), so eliminate.

Step3: Check Option 2 (-1 and -25)

Multiply: \( (-1)\times(-25) = 25
eq30 \). Also, \( 25 \) does not divide \( 30 \) ( \( 30\div25 = 1.2 \) ), so eliminate.

Step4: Check Option 3 (-2 and -17)

Multiply: \( (-2)\times(-17)=34
eq30 \). \( 34 \) does not divide \( 30 \), so eliminate.

Step5: Check Option 4 (-3 and -10)

Multiply: \( (-3)\times(-10)=30 \). Now check if they are factors of \( 30 \): \( 30\div(-3)= - 10 \) (integer), \( 30\div(-10)= - 3 \) (integer). So both are factors.

Answer:

D. -3 and -10 (assuming the options are labeled A to D as 0 and -30, -1 and -25, -2 and -17, -3 and -10 respectively)