## Math 6A, Lesson 2, Fall 2020, 9/20/2020

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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)