Question 1: Construct a factor tree for the number 84, which could represent the total number of pills in a medication batch. Find its prime factors.

Answer: 2 × 2 × 3 × 7

Question 2: Using a factor tree, determine the prime factors of 126, which could represent the dosage units in a medical supply.

Answer: 2 × 3 × 3 × 7

Question 3: Construct a factor tree for the number 100, which could represent the total number of health supplements in a shipment.

Answer: 2 × 2 × 5 × 5

Question 4: Construct a factor tree for 210, representing the total number of medicines in a pharmacy inventory. Find its prime factors.

Answer: 2 × 3 × 5 × 7

Question 5: Explain why constructing factor trees helps in understanding the composition of medication quantities in health sciences.

Answer: Factor trees break down composite numbers into prime factors, revealing their basic building blocks. This helps in understanding how different medicine dosages or quantities are related or can be combined or divided efficiently.

Question 6: A pharmacy receives a shipment of 360 pills. Use a factor tree to find its prime factors. How could this help in packaging the pills into smaller doses?

Answer: 2 × 2 × 2 × 3 × 3 × 5

Question 7: A medicine bottle contains 144 tablets. Construct a factor tree and determine the prime factors. How can prime factorization assist in dividing tablets into smaller doses?

Answer: 2 × 2 × 2 × 2 × 3 × 3

Question 8: A hospital orders 495 units of a medication. Using a factor tree, find the prime factors and discuss how this helps in understanding the distribution of medication packages.

Answer: 495 = 3 × 3 × 5 × 11. Knowing the prime factors helps in dividing the total units into smaller, evenly sized packets, simplifying distribution.

Question 9: Identify and correct the mistake in this factor tree for 84: 84 / \ 2 42 / \ 6 7 / \ 2 3

Answer: The mistake is in factoring 6 into 2 and 3; 6 should be further broken down into 2 and 3, which is correct, but the tree incorrectly shows 42 as 6 × 7 without breaking 42 into prime factors. The correction is to show 42 as 2 × 3 × 7.

Question 10: Construct a factor tree for 180 and list all prime factors. Then, explain how understanding these factors could help in preparing equal doses of medication.

Answer: 180 = 2 × 2 × 3 × 3 × 5. Knowing these factors allows for dividing 180 into smaller, equal doses or units, ensuring accurate medication distribution.