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:

Step 1: Find factors of 54

The factors of 54 are the numbers that divide 54 without leaving a remainder. We list them: \(1, 2, 3, 6, 9, 18, 27, 54\).

Step 2: Find multiples of 6

Multiples of 6 are numbers like \(6, 12, 18, 24, 30, \dots\) (obtained by multiplying 6 by integers: \(6\times1 = 6\), \(6\times2 = 12\), \(6\times3 = 18\), etc.).

Step 3: Find the common number

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

• 3: Factor of 54? Yes. Multiple of 6? No (\(3\div6 = 0.5\), not an integer).
• 9: Factor of 54? Yes (\(54\div9 = 6\)). Multiple of 6? No (\(9\div6 = 1.5\), not an integer).
• 12: Factor of 54? No (\(54\div12 = 4.5\), not an integer). Multiple of 6? Yes (\(12\div6 = 2\)).
• 18: Factor of 54? Yes (\(54\div18 = 3\)). Multiple of 6? Yes (\(18\div6 = 3\)).

So 18 is a factor of 54 and a multiple of 6.

Answer:

The correct option is the one with 18 (the bottom - right option). In terms of the options as presented (assuming the options are: top - left: 3, top - right: 9, bottom - left: 12, bottom - right: 18), the answer is the option with 18 (the bottom - right circle - labeled option with 18). If we consider the options as labeled (though not explicitly labeled with letters here, but by position): the bottom - right option (the one with 18) is the correct answer. So in boxed form (assuming we are to box the number), \(\boxed{18}\)