1. Factors
􀀹 Use the prime factorization of two whole numbers to determine the greatest common factor and the least common multiple.

2. Factors
Factor: Any one of the numbers multiplied in a multiplication problem.
Factor: A whole number that divides another whole number without a remainder.

3. Prime Numbers
A counting number greater than 1, whose only two factors are the number 1 and itself.
Examples:
2: 1x2
3: 1x3
5: 1x5
7: 1x7
11: 1x11

4. Composite Number
A counting number greater than 1 that is divisible by a number other than itself and 1.
Every composite number has at least three factors.
Every composite number can be expressed as a product of two or more prime numbers.
Examples:
4: 1, 2, 4
6: 1, 2, 3, 6

5. Greatest Common Factor (GCF)
The largest whole number that is a factor of two or more given numbers.
Example
15: 1, 3, 5, 15
20: 1, 2, 4, 5, 10, 20
What factors do 15 and 20 have in common?
1 and 5
Which one of the factors is greatest or largest?
5, therefore 5 is the Greatest Common Factor

6. Least Common Multiple (LCM)
The smallest whole number that is a multiple of two or more given numbers.
Reminder: A multiple is a product of a counting number and another number.
Example:
The multiples of 3: 3, 6, 9, 12, 15, 18, 21, …

7. LCM Find the LCM of 4 and 6 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
What multiples do 4 and 6 have in common?
12, 24, 36
Which is the least or smallest? 12

8. Your Turn Find the Greatest Common Factor of 12 and 15.
12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
The GCF of 12 and 15 is 3
Find the Least Common Multiple of and 8.
6: 6. 12, 18, 24, 30, …
8: 8, 16, 24, 32, 40, …
The LCM of 6 and 8 is 24