Question

a factor is a number that divides into another number evenly, with no remainder. which four numbers are all factors of 24? 2 and 12 -3 and -8; 2 and -12 9 and -3; -5 and -6 3 and 8; -6 and -4 12 and 3

Explanation:

Step1: Recall the definition of a factor

A factor of a number \( n \) is an integer \( k \) such that \( \frac{n}{k} \) is also an integer (no remainder). For positive and negative factors, if \( k \) is a factor of \( n \), then \( -k \) is also a factor because \( \frac{n}{-k}=-\frac{n}{k} \), which is an integer if \( \frac{n}{k} \) is an integer.

Step2: Check each option for factors of 24

• Option 1 (2, 12, -3, -8):
• Check \( 24\div2 = 12 \) (integer, so 2 is a factor).
• Check \( 24\div12 = 2 \) (integer, so 12 is a factor).
• Check \( 24\div(-3)= - 8 \) (integer, so -3 is a factor).
• Check \( 24\div(-8)= - 3 \) (integer, so -8 is a factor).
• Option 2 (2, -12, 9, -3):
• \( 24\div9=\frac{8}{3}\) (not an integer, so 9 is not a factor).
• Option 3 (-5, -6, 3, 8):
• \( 24\div(-5)=-\frac{24}{5}\) (not an integer, so -5 is not a factor).
• Option 4 (-6, -4, 12, 3):
• Wait, the first option already has all four numbers as factors. Let's re - check the first option:
• \( 24\div2 = 12\), \( 24\div12 = 2\), \( 24\div(-3)=-8\), \( 24\div(-8)=-3\). All divisions result in integers, so 2, 12, - 3, - 8 are all factors of 24.

Answer:

The four numbers that are all factors of 24 are 2, 12, - 3, - 8 (the first option: 2 and 12, - 3 and - 8).