Review Test #2 Ch. 4&5 Math 1315
Prime Power Representation
600=2*2*2*3*5*5= 2^2+3^1+5^2
Greatest Common Divisor (GCF)
A & B are whole #'s that cannot=0. The greatest natural number (factor) D that divides into both A & B is called their Greatest Common Divisor or greatest common factor of a and b. GCD=(12,18)=6 Find the greatest common divisor of 270 and 630. ....(see pp ch 4). Notice that we only work with the factors that are common to the two numbers. Then we choose the lowest power on each common factor.
Unit
A unit is equal to the number one since it is neither prime nor composite, and it has exactly one factor.
Odd Number
A whole number ending with 1, 3, 5, 7, or 9 in the ones place. (not divisible by 2).
Even Number
A whole number is even when it is divisible by 2.
Prime Number
A whole number that has exactly two factors, 1 and itself. The #2 is the only even prime #.
Composite Number
A whole number that have more than two factors.
How to find the Number of Factors
Ex:300 Find is factor tree prime factorization, IN its Power form. Power of 2,1,&2. Now take these exponents and add 1 to them. Ex: 2+1=3 1+1=2 2+1=3. Now multiply those numbers together: 3*2*3=18. 18 is the number of factors of 300. Answer:18 factors
Divisible by 12
If its last 2 digits are divisible by 4 and the sum of its digits is divisible by 3. Ex:48/4=12 & 4+8= 12/3=4.
Divisible by 25
If last 2 digits are divisible by 25. Ex: 25,50,75.
Divisible by 4
If the last 2 digits are divisible by 4 Ex:332 is divisible by 4 bc 32/4=8
Divisible by 8
If the last 3 digits are divisible by 8. Ex:2,144= 144/8=18.
Divisible by 5
If the last digit is 0 or 5. Ex=19875/5 = 3,975
Divisible by 20
If the last two numbers are: 20,40,60,80,00 ;)
Divisible by 16
If the number formed from the last four digits is divisible by 16.
Divisible by 2
If the ones place is either (0,2,4,6,or 8). Ex: 68 is divisible by 8 because 8 is even.
Divisible by 3
If the sum of all its digits is divisible by 3. Ex: 21 = 2+1=3
Divisible by 9
If the sum of the digits is divisible by 9. Ex:135= 1+3+5=9.
Divisible by 15
If units digit/ones place is 0 or 5, and if the sum of the digits is divisible by 3. Ex:30 ends in 0. 30/3=10.
Divisible by 22
If units digit/ones place is even and if the difference between the sums of very other digit is divisible by 11.
Least Common Multiple (LCM)
Let a and b be natural numbers. The least natural number that is a multiple of both a and b is called their least common multiple, and we write: LCM(a,b). LCM in bigger #'s is the product of the highest powers of any factor on either number.
Divisibility Rules
Rules that tell if one whole number is divisible by another.
Factor Tree Example
See image.
Divisible by 11
Starting in the ones place add every other digit and remember this #. Form a new # by adding the digits that remain. If the difference between these two numbers is divisible by 11, then its divisible by 11. ex:528 Sum of 8+5=13 Sum of 2=2 13-2=11 Therefore 528 is divisible by 11.
Absolute Value
The absolute value of a number is its distance from zero. Absolute value is also called magnitude.
Additive Inverse of a Number
The additive inverse of a number is the same as the opposite of the number aka the sum of a number and its opposite is 0. Ex: 5=-5 etc. *ZERO is the ONLY number that is it's own opposite.
Divisible by 10
The number ends in 0. Aka: Zero in ones place. Ex:1349780/10. Yes.
Divisible by 6
The number is divisible by both 2 and 3. The ones place is even & the sum of the digits is divisible by 3. Ex:36/2=16 36= 3+6= 9/3=3
What is the number (limit) of prime numbers?
There is no limit. Prime numbers are infinite. "oo".
Relatively Prime
Two numbers are "relatively prime" when they have no common factors other than 1. Ex:The factors of 32 are 1,2,4,8,18,32. The factors of 75 are 1,3,5,15,25,75. The only number they have in common is the number 1, therefore 32 &75 are relatively prime.
