Date post: | 24-Dec-2015 |
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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.
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…”
Greatest Common Divisor of 15 & 45
3 5 45
3 15
3 52 1
3 53
15
3 5
3 51 1
Maximum number of common factors in each final row is one three and one 5
Therefore, the GCD is 3*5 = 15
GCD is 15
Greatest Common Divisor of 8 & 27
Note: there is
no Common Divisor,
8
2 4
23
2 22
27
3 9
33
3 33
What number divides all numbers evenly?
1
Therefore,The GCD =1
TEST YOURSELF
1. 12 & 182. 12 & 243. 18 & 324. 32 & 645. 12 & 546. 18 & 54
7. 18 & 648. 32 & 549. 24 & 6410.54 & 7211.14 & 15
Find the GCD for the following pairs of numbers
612232618
228181
Exponents
Repeated Multiplication be
So you would multiply b e times b*b*b*b*b*…*b {e times}
b = base e = exponent
Rules of Exponents:
Qty raised to an Exp
(ab)m
(3x)4
Distribute exponents
ambm
34x4
Quantity to an Exponent
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
Terminology
Factor Prime number Composite number Prime Factorization Exponential Form Greatest Common
Divisor
Expanded Form Sum Difference Product Quantity Reciprocal
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