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What is the longest string of numbers you can create without repeat following the given rules below:
What is the longest string of numbers you can create without repeat following the given rules below:
Rule 1: Each number in the sequence must be a factor or multiple of the previous number.
Rule 1: Each number in the sequence must be a factor or multiple of the previous number.
Rule 2: You may only use the numbers 1-100.
Rule 2: You may only use the numbers 1-100.
Rule 1: A number in the sequence may not be repeated.
Rule 1: A number in the sequence may not be repeated.
*Click on the grid for a printable student worksheet
Directions
Directions
1. Select a number from 1-100. Cross it off.
1. Select a number from 1-100. Cross it off.
2. Then choose a factor or multiple of that number.
2. Then choose a factor or multiple of that number.
3. Keep crossing out factors or multiples of the last number in the chain. For example Ricky started with 50, 100, 5, 10, 20, 40....
3. Keep crossing out factors or multiples of the last number in the chain. For example Ricky started with 50, 100, 5, 10, 20, 40....
4. What's the longest string of numbers you could make?
4. What's the longest string of numbers you could make?
5. When you're finished, answer the questions in the box below.
5. When you're finished, answer the questions in the box below.
Example Sequence
Example Sequence
6, 30, 60, 10, 5...
Jeremy starts with the number 6.
Next he decides to use the number 30 since 30 is a multiple of 6.
Next Jeremy decides to use the number 60 since 60 is a multiple of 30.
Since the next multiple of 60 is 120 which is larger than 100, Jeremy has to use a factor of 60 so he chooses 10.
Next, Jeremy decides to use a factor of 10 so he chooses 5.
Jeremy will continue listing factors and multiples until he has no numbers left over from which to choose that are factors or multiples of the previous number.
Questions to Consider
Questions to Consider
- What strategies led you to creating your longest string?
- What numbers of types of numbers were most useful to you generating your longest string?
- What numbers of types of numbers were the least helpful to you generating your longest string?
- Is it possible to generate a list that includes all 100 numbers? Why or why not?
Check Your Answer!
Check Your Answer!
Use the link to the left to check your solution!
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