Ahmed has 14 pens and 42 notebooks. What is the maximum number of friends he can distribute them to? Should he use GCF or LCM? Additionally, find the product of 8 and 17, and the p... Ahmed has 14 pens and 42 notebooks. What is the maximum number of friends he can distribute them to? Should he use GCF or LCM? Additionally, find the product of 8 and 17, and the product of 9 and 12.
Understand the Problem
The question is asking how to solve a math problem that involves finding the maximum number of friends Ahmed can distribute pens and notebooks to based on given conditions related to GCF and LCM. It also involves finding products using specific numbers.
Answer
14
Answer for screen readers
Ahmed can distribute the pens and notebooks to a maximum of 14 friends.
Steps to Solve
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Identify the quantities
Ahmed has 14 pens and 42 notebooks. -
Find the GCF (Greatest Common Factor)
To find the maximum number of friends he can distribute items to equally, we calculate the GCF of the two numbers, 14 and 42.The factors of 14 are: 1, 2, 7, 14
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42The common factors are: 1, 2, 7, 14
Thus, $GCF(14, 42) = 14$. -
Maximum distribution
Since the GCF is 14, Ahmed can distribute both the pens and the notebooks to 14 friends. -
Confirm equal distribution
Each friend will receive:- $ \frac{14 \text{ pens}}{14 \text{ friends}} = 1 \text{ pen per friend} $
- $ \frac{42 \text{ notebooks}}{14 \text{ friends}} = 3 \text{ notebooks per friend} $
This means that both items are distributed evenly among 14 friends.
Ahmed can distribute the pens and notebooks to a maximum of 14 friends.
More Information
Distributing items using GCF ensures that every friend gets an equal share, optimizing the use of available items.
Tips
- Not calculating GCF correctly: Ensure all factors are considered when finding the GCF.
- Overlooking equal distribution: Verify that both items can be fairly distributed using the calculated GCF.
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