1. Greatest Common Divisor Exponents Sections 1.2 & 1.3
Review of Numbers
Greatest Common Divisor
Exponents
Sections 1.2 & 1.3

2. Whole Previous Information Types of numbers Natural Integers Rational
Irrational

3. Purpose
In later mathematics, you will want to work with numbers in simplest form.
It is easier to work with small numbers rather than large numbers.

4. Prime Factorization
Breaking a number down into it’s combination of prime factors
To start prime factorization, ask yourself…
“Will 2 divide this number…,
Will 3 divide this number…,
Will 5 divide this number…”

5. Factors of 15 15 15 3 5 3 5 3 5 3 5 Alternate Method Factor Tree 3 5 1

6. Factors of 45 45 45 3 15 3 3 15 5 3 5 3 3 5 3 5 Alternate Method
Factor Tree 3 5 45 45 3 15 3 3 15 5 2 1 3 5 3 3 5 2 1 3 5

7. Greatest Common Divisor
Largest factor of 2 or more numbers
When finding – use prime factorization

8. Greatest Common Divisor of 15 & 453 5 45 15
Maximum number of common factors in each final row is one three and one 5 3 15 3 5
Therefore, the GCD is 3*5 = 15 3 3 5 1 1 3 5
GCD is 15 2 1 3 5

9. Greatest Common Divisor of 8 & 27
Note:
there is no Common Divisor, 8 27
Therefore,
The GCD =1 2 4 3 9
What number divides all numbers evenly? 2 2 2 3 3 3 1 3 3 2 3

10. TEST YOURSELF
Find the GCD for the following pairs of numbers
12 & 18
12 & 24
18 & 32
32 & 64
12 & 54
18 & 54
18 & 64
32 & 54
24 & 64
54 & 72
14 & 15 6 12 2 32 18 2 8 18 1

11. Exponents Repeated Multiplication be b = base e = exponent
So you would multiply b  e times
b*b*b*b*b*…*b {e times}

12. Examples 24 72 x3
=2*2*2*2
=7*7
=x*x*x
=16
=49
= x3

13. Rules of Exponents: MULTIPLICATION
Add exponents
am+n
32+4 = 36
Multiply like Bases
am * an
32 * 34

14. Rules of Exponents: Exponents
Multiply exponents
am*n
32*4= 38
Exp raised to an Exp
(am )n
(32)4

15. Rules of Exponents: DIVISION
Subtract exponents
am-n
34-2 = 32
Divide like Bases am an 34 32

16. Distribute exponents Qty raised to an Exp ambm (ab)m (3x)4 34x4
Rules of Exponents:
Quantity to an Exponent
Distribute exponents
ambm
34x4
Qty raised to an Exp
(ab)m
(3x)4

17. Rules of Exponents: Negative Exp
= the reciprocal 1 am
Number raised to a neg Exp
a-m
3-2 =

18. TEST YOURSELF: Rules of Exponents
23 * 24
54/53
(2/5)2
-32
(-3)2
(6x)3
6x3
7(-2)
23+4 = 27 = 128
54-3 = 51 = 5
22/52 = 4/25
-32 = -9
(-1)2 * 32
63x3 = 216x3
6x3
1/72 = 1/49

19. Terminology Factor Prime number Composite number Prime Factorization
Exponential Form
Greatest Common Divisor
Expanded Form
Sum
Difference
Product
Quantity
Reciprocal

20. Conclusion Any two are more numbers have a Greatest Common Divisor
(either 1 or some other Factor)
To find the GCD use Prime Factorization
(match factors using the smallest exponential value)
Rules of Exponents

21. Assignment
On-line
12 GCD & Exponents