Introduction
On a television show that you are watching, you notice quite often that the detectives need clues within the first 48 hours to solve a crime. If they don’t get a clue within the first 48 hours, it is likely that the case may turn cold. Detectives work very hard during the first 48 hours.
Since there are only two detectives on this case, they need to split the time equally among different witnesses. How many witnesses could they interview and allocate the same amount of time to them? What would be the minimum number and minimum amount of witnesses they could interview within the first 48 hours.
You will need to use the factors of 48 to find the answer. That would be the easiest way to figure out this situation for the detectives. See if you can do that.
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Finding the Factors of 48
Number 48 has quite a few factors mainly since it is an even number. However, there are other reasons too. It is a multiple of 12 which is a popular number as many things are grouped into dozens. A way to find the factors of 48 would be to list all the numbers from 1-48 like the list below. Then you can be assured that all factors will be included.
You need to determine if each number can equally divide into 12. There should be no remainder. You may need to use a calculator. Work a division problem for each one. If there is a remainder for that problem, then it is not a factor. All the other numbers that do equally divide into 48 without remainders would be considered factors of 48. Remember a factor always has a factor partner. When you multiply the factor number and its partner together, you will get the number, 48. Sometimes, a factor’s partner can be itself.
The numbers with a remainder should be eliminated because they are not factors of 48. You should check each factor by matching it with its factor partner. So, when they are multiplied together, they will equal 48. Below shows the factor number and its partner, which is also a factor of 48.
Back to the detective situation, you can solve this problem now that you know the factors of 48. Since there are 10 factors for 48, then the detective could have 10 different combinations of witnesses and hours. They could have 1 witness and interview them for 48 hours or 1 hour each for 48 witnesses. Both of these would be the least and highly unlikely. The detectives could interview or question 2 witnesses at 24 hours each or 2 hours for 24 witnesses. They could interview 3 witnesses for 16 hours each or 3 hours for 16 witnesses. They could interview 4 witnesses at 12 hours each or 12 witnesses at 4 hours each. Last, they could interview 6 witnesses at 8 hours each or 8 witnesses at 6 hours each.
Challenging Questions
Question 1List the factors of 48
Which positive whole numbers divide 48 without leaving a remainder?
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 48
Which multiplication pairs have a product of 48?
48 has these positive factor pairs: 1 × 48; 2 × 24; 3 × 16; 4 × 12; 6 × 8.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 48
What is the prime factorization of 48?
48 = 2 × 2 × 2 × 2 × 3.
Every number in the product is prime.
