Introduction
As a pharmacist, Gerald must dispense a certain amount of drugs that have been prescribed to a patient. The prescription shows how much of the medicine the patient is required to have. Gerald takes that prescription and makes sure that the prescription is created exactly as stated. Therefore, there are times that pills must be cut in half or ground to a powder in order for the person to get the exact dosage. In Gerald’s case, the patient’s prescription requires that each dosage contains 45 milligrams of the medicine in a pill. However, Gerald’s pills come in 81 milligrams each. Gerald realizes that he needs to crush up some of 81-milligram pills into smaller sections. Then pour 45 milligrams of the pill powder into separate containers. Each container will be a separate dosage for his patient. Use the factors of 81 to solve Gerald’s situation.
Finding the Factors of 81
The factors for the number, 81, are only five. It is not an even number, so that eliminates 2 being a factor. Most numbers have an even number of factors because each factor has a partner. When multiplied together, they will equal the original number. However, a few numbers, like 81, have a factor that have the same factor partner.
Let’s find out the factors for eighty-one. To find out, we will see which numbers 81 or fewer can equally divide into 81. The number will not be a factor of 81 if there is a remainder when dividing. Let’s gather the factors!
Since there are not a lot of factors for 81, it is always best to look twice at the factors when you realize that you have only a few factors for a number.
So, Gerald needs to use the factors of 81 which are 1, 3, 9, 27, and 81. To do this, he first needs to grind the 81-milligram pills into a powder. Then divide it into 9 equal groups. Using the factors of 81, you will know that in each group, there will be 9 milligrams of medicine because 9 times 9 equals 81. Now, Gerald needs 45-milligrams in a pouch, so take 5 groups of 9-milligrams and put it into a pouch. You will have 4 groups of 9 milligrams of medicine left or 36 milligrams. So, Gerald doesn’t waste any of the medicine, you need to make sure that all of the medicine is used up. You need to see a common amount for both 45 and 81. In this case, it is 810. So, take 9 more pills and crush them, then you can make 18 pouches with 45-milligrams in each.
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Challenging Questions
Question 1List the factors of 81
Which positive whole numbers divide 81 without leaving a remainder?
The factors of 81 are 1, 3, 9, 27, 81.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 81
Which multiplication pairs have a product of 81?
81 has these positive factor pairs: 1 × 81; 3 × 27; 9 × 9.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 81
What is the prime factorization of 81?
81 = 3 × 3 × 3 × 3.
Every number in the product is prime.
