QuestionWhat do you notice about the number of possible arrays and the number of factors of 22?
Studdy Solution
STEP 1
1. The problem involves understanding the relationship between the number of possible arrays and the number of factors of the number 22.
2. An array can be thought of as a rectangular arrangement of elements, where the dimensions of the array are factors of the total number of elements.
3. The number of possible arrays corresponds to the pairs of factors of the number 22.
STEP 2
1. Determine the factors of 22.
2. Pair the factors to form possible arrays.
3. Compare the number of possible arrays to the number of factors.
STEP 3
Identify the factors of 22. Factors are numbers that divide 22 without leaving a remainder.
The factors of 22 are: and .
STEP 4
Pair the factors to form possible arrays. Each pair represents the dimensions of a possible array.
Possible pairs (arrays) are:
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STEP 5
Count the number of unique arrays and compare it to the number of factors.
There are 4 factors of 22, and there are 2 unique pairs of factors that form arrays: and .
The observation is that the number of unique arrays (2) is half the number of factors (4) because each array can be represented by a pair of factors, and each pair is counted twice (once in each order).
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