Working with a partner, study the following number pattern in Pascal's triangle.
Exploring Pascal's Triangle
Questions, Answers, and Discussion
Notice that the gray cell is surrounded by 6 other cells. These six cells make up the petals on Pascal's flower.
Starting with the petal above and to the left of the gray center, alternating petals are colored yellow and numbered 5, 20, and 21.
The three remaining petals around the chosen center are colored orange and numbered 6, 10, and 35.
The product of the numbers in the yellow petals is 5 x 20 x 21 = 2100.
The product of the numbers in the orange petals is 6 x 10 x 35 = 2100.
The products are the same. Can you explain this? When you write the prime factorizations you will see that the cells contain all the same factors.
Write the prime factorization of each of the numbers in the yellow petals.
5, 2 x 2 x 5, 3 x 7 or 22 x 3 x 52 x 7
Write the prime factorization of each of the numbers in the orange petals.
2 x 3, 2 x 5, 5 x 7 or 22 x 3 x 52 x 7
Compare the prime factorizations of the two sets of numbers. Write an explanation of your discovery. The prime factorizations can be more easily compared if the factors are written in order from smallest to largest using exponents for repeated factors.
Share your discoveries with the group.
What if a different center number were chosen? Would the results be the same?
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