Question

a factor is a number that divides into another number evenly, with no remainder. factors also include negative numbers. which three numbers are factors of 120? -6, 10, -12; 0, 17, -19; -7, 13, -21; -9, 14, -22

Explanation:

Step1: Recall the definition of a factor

A factor of a number \( n \) is an integer that divides \( n \) without leaving a remainder. This includes both positive and negative integers.

Step2: Check each option

• Option 1: -6, 10, -12
• Check if \(-6\) divides \(120\): \(120\div(-6)= - 20\), which is an integer with no remainder.
• Check if \(10\) divides \(120\): \(120\div10 = 12\), which is an integer with no remainder.
• Check if \(-12\) divides \(120\): \(120\div(-12)=-10\), which is an integer with no remainder.
• Option 2: 0, 17, -19
• Division by \(0\) is undefined, so \(0\) cannot be a factor of \(120\).
• Check if \(17\) divides \(120\): \(120\div17\approx7.058\), which is not an integer.
• Check if \(-19\) divides \(120\): \(120\div(-19)\approx - 6.315\), which is not an integer.
• Option 3: -7, 13, -21
• Check if \(-7\) divides \(120\): \(120\div(-7)\approx - 17.14\), which is not an integer.
• Check if \(13\) divides \(120\): \(120\div13\approx9.23\), which is not an integer.
• Check if \(-21\) divides \(120\): \(120\div(-21)\approx - 5.71\), which is not an integer.
• Option 4: -9, 14, -22
• Check if \(-9\) divides \(120\): \(120\div(-9)\approx - 13.33\), which is not an integer.
• Check if \(14\) divides \(120\): \(120\div14\approx8.57\), which is not an integer.
• Check if \(-22\) divides \(120\): \(120\div(-22)\approx - 5.45\), which is not an integer.

Answer:

1. -6, 10, -12