Question

relating factors and multiples ii - item 1759
which number is a factor of 54 and a multiple of 6?
3
9
12
18

Explanation:

Step1: Find factors of 54

The factors of 54 are the numbers that divide 54 without leaving a remainder. We find them by dividing 54 by integers starting from 1:

• \(54\div1 = 54\), so 1 and 54 are factors.
• \(54\div2 = 27\), so 2 and 27 are factors.
• \(54\div3 = 18\), so 3 and 18 are factors.
• \(54\div6 = 9\), so 6 and 9 are factors.

So the factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54.

Step2: Find multiples of 6

Multiples of 6 are numbers that can be written as \(6\times n\) where \(n\) is an integer. Let's list some multiples of 6:

• \(6\times1 = 6\)
• \(6\times2 = 12\)
• \(6\times3 = 18\)
• \(6\times4 = 24\)
• etc.

Step3: Find the common number

Now we check which number from the options (3, 9, 12, 18) is both a factor of 54 and a multiple of 6.

• 3: It is a factor of 54 (as we saw in Step1), but is 3 a multiple of 6? \(3\div6 = 0.5\), which is not an integer, so 3 is not a multiple of 6.
• 9: It is a factor of 54, but \(9\div6 = 1.5\), not an integer, so 9 is not a multiple of 6.
• 12: Is 12 a factor of 54? \(54\div12 = 4.5\), not an integer, so 12 is not a factor of 54.
• 18: It is a factor of 54 (from Step1: \(54\div18 = 3\)), and it is a multiple of 6 (\(18\div6 = 3\), which is an integer, so \(18 = 6\times3\)).

Answer:

18 (the option corresponding to 18, which should be the one with the radio button next to 18)