Adjust the numbers in the Summarizing the Lesson activity to meet the needs of individual students. For students who are having difficulty finding prime factorizations for larger numbers, have them find factor trees for smaller numbers, such as 18, 27, 32, and 45. When finding the numbers with the most prime factors, reduce the range to between 2 and 50. Use larger numbers and ranges for students who are ready for more challenging tasks.
Provide additional practice finding prime factorizations by asking students to make factor trees for the numbers:
42, 70, 120, 196, and 1000
Have students work with partners to find factor trees for other numbers they choose between 2 and 100.
- Which number or numbers between 1 and 100 have
the most prime factors, including repeated factors?
(64 has six prime factors: 2 × 2 × 2 × 2 × 2 × 2.)
- Which number or numbers between 1 and 100 have the most different prime factors, not including repeated factors? For example, the prime factorization of 12 is 2 × 2 × 3, so 12 has two different prime factors: 2 and 3. (30, 42, 60, 66, 70, 84, and 90 each have three different prime factors.)
