The correct answers are:
\(1, 48;
\\2, 24;
\\3, 16;
\\4, 12;\text{ and }
\\6, 8\)
Explanation:
We can use our divisibility rules to find the factors of 48. First off, we know that 1 is a factor of every number; to make 48 from 1, we multiply 1(48).
Since 48 is even, that means 2 is a factor; 48/2 = 24, so 2 and 24.
For 3, check the sum of the digits. 4+8 = 12; this is divisible by 3, so 48 is divisible by 3. 48/3 = 16, so we have 3 and 16.
For 4, since it is a two digit number, we just have to manually check. 4 goes into 4, and 4 goes into 8, so 4 goes into 48. 48/4 = 12, so we have 4 and 12.
For 5, the number does not end in 5 or 0, so it is not divisible by 5.
For 6, we check for divisibility by 2 and 3. Since it is divisible by both, then it is divisible by 6. 48/6 = 8, so we have 6 and 8.
For 7, since it is such a small number, we can just check. It is not divisible by 7.
We know from earlier that 48 is divisible by 8; 48/6 = 8, so 48/8 = 6. Since we have begun to repeat factors, we are finished.
