**Math 6A, Lesson 2, Fall 2017, 9/17/2017**

**1. Greatest Common Factor (GCF)**: the largest common factor of a group of numbers is the largest positive integer that can divide all the numbers in the group.

The factors of 18: 1, 2, 3, 6, 9, 18

The factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

1, 2, 3, and 6 are called** the common factors **of 18 and 24. The largest of these common factors is 6. Thus, 6 is **the greatest common factor** of 18 and 24.

**HCF**: the highest common factor, same as GCF

**GCD**: the greatest common divisor, same as GCF

**Relatively Prime or Mutually Prime**: when two numbers, such as 15 and 16, have no common factors greater than 1, their GCF = 1 and the numbers are said to be relatively prime, or mutually prime.

**2. Methods to find GCF**

- Using prime factorization. GCF is obtained by multiplying the lowest power of each common factor of the given numbers. Teaching on whiteboard in the class.
- Continuous division. Teaching on whiteboard in the class.
- Venn diagram. Teaching on whiteboard in the class.

**3. Why GCF?**

- Reduce a fraction to its lowest terms: 18/48 = (18 / 6) / (48 /6) = ⅜
- Algebra, GCF of the coefficients: 18x*x + 48x = 6x(3x + 8)
- Word problems: Teaching on whiteboard in the class

**4. Home Work:**

- Handout: one page
- Workbook:
- page 2: 6, 10(a), 10(b), 11
- Page 3: 12, 14, 15(a), 15(b)(i), 17(a), 17(b)(i)
- Page 4: 21, 22
- Page 5: 26, 27, 28, 29(b)