11 m is a multiple of 8 and a factor of 48. List all the possible values of m.
The Correct Answer and Explanation is:
To find all possible values of mmm, we need to determine which numbers meet the following two conditions:
- mmm is a multiple of 8.
- mmm is a factor of 48.
Step 1: Identify multiples of 8
Multiples of 8 are numbers that can be written as 8k8k8k, where kkk is an integer. So, the multiples of 8 are:8,16,24,32,40,48,56,64,…8, 16, 24, 32, 40, 48, 56, 64, \dots8,16,24,32,40,48,56,64,…
We need to check which of these multiples of 8 also divide 48 evenly.
Step 2: Identify factors of 48
To find the factors of 48, we start with its prime factorization:48=24×348 = 2^4 \times 348=24×3
Now, the factors of 48 are all the numbers that can be formed by multiplying these prime factors in different combinations. The factors of 48 are:1,2,3,4,6,8,12,16,24,481, 2, 3, 4, 6, 8, 12, 16, 24, 481,2,3,4,6,8,12,16,24,48
Step 3: Find common values
We now find the common numbers between the multiples of 8 and the factors of 48. From the two lists above, the multiples of 8 that are also factors of 48 are:8,16,24,488, 16, 24, 488,16,24,48
Conclusion
The possible values of mmm are:8,16,24,488, 16, 24, 488,16,24,48
These are the numbers that satisfy both conditions: they are multiples of 8 and factors of 48.
