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LCM (Least Common Multiple/Factor) Steps:
 1) Determine the prime #s
 2) Take each prime factor to the highest power it appears.
 3) Multiply together the results of the primes to their highes power

Universal Divisibility Strategy:
Simply subtract easy to identify multiples of that # until you recognize a factor or nonfactor, or 0.
ex. 952 divisible by 7?
 952  700 = 252 >
 252  210 = 42 >
 4242 = 0 (thus yes, divisible by 7)

Divisibility rule 3:
# is divisible by 3 if the sum of the digits is a multiple of 3

Divisibility rule 4:
# is divisible by 4 if last two digits together is divisible by 4. Ex: 724

Divisiblity rule 6:
# is divisible by 6 if even AND sum of digits divisible by 3

Divisibility rule 9:
# is divisible by 9 if sum of digits is a multiple of 9

Divisibility rule 11:
# is divisible by 11 if difference b/w sums of alternate digits is divisible by 11
 ex: 4,983 divisible by 11?
 4+8 = 12
 9+3 = 12
 1212 (diff b/w sums) = 0
Thus yes 4,983 is divisible by 11

Prime factors vs. Unique Factors:
How many prime factors does 20 have?

Prime factors vs. Unique Factors:
How many unique factors does 20 have?
Figure out factors working from greatest to least (outside > in pairs)
20, 10, 5, 4, 2, 1
Unique factors = 6

Comparing Fractions:
A vs C
B vs D
Multiply denominators for common denominator, then cross multiply numerators

Comparing Fractions  which is greater?
3 vs 11
7 vs 25
best way?
Since denominators will be the same, just skip calc & compare numerators after cross multiply.
 3x25=75  7x11=77
 75 or 77 greater? 77 so... 11/25 greater

What is the distance/rate or Work/Rate formula?
D=RT or W=RT

What is the "trick" to calculating rate?
Rate is the inverse of time (only when talking about a full job).
ex. T = 6hrs, R = 1/6th per hour

What are the 5 important steps to rates?
 1) Always convert time to rates
 2) Rates are additive
 3) Once you have the necessary rate, plug in the info to W=RT to solve.
 4) When conditions change, reset equations & solve with multiple equations (not one)
 5) Recognize if the rate is the same, then time used is proportional to # of workers. More workers = less time & vice versa.

% of =
% of = (part/whole) x 100


% Change =
% Change = (New value  Orig Value)/ Orig Value x 100

Greatest common factor/steps?
 1) Factor out the #s into primes
 2) Pick the prime #s out that they both share (only)
 3) Multiply those prime #s together (only once for ea. #).

What's this definition for..."The smallest nonzero # that is a multiple of two or more #s"
LCM (least common multiple)

What's this definition for... "The largest # that divides evenly into each of a given set of #s"
GCF (Greatest common factor or divisor)


