# Prime factorizations

Complete the following tasks.

- Create a Venn diagram using the prime factorization of 48 in one set and the prime factorization of 72 in the other set.
- The LCM and GCF are given. Explain how you could use the Venn diagram to obtain the same answers.
- LCM(48, 72) = 144
- GCF(48, 72) = 24

- Next, we will explore a conjecture about LCM and GCF.
- What is the product of 12 and 100?
- What is the product of LCM(12, 100) and GCF(12, 100)?
- Provide a conjecture based on the previous results.
- Use prime factorizations to justify why the conjecture might be true.

## Challenge problems

- Will the LCM GCF conjecture work for three numbers? Pick three numbers to see.

No.

LCM(8, 10, 12) = 120

GCF(8, 10, 12) = 2

8 * 10 * 12 = 960 != 2 * 120
- Construct three numbers, each with exactly seven factors.
- How many two-digit numbers have 8 factors? Justify your answer. (difficult question!)