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Terms in this set (41)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
How Many Factors?
To find how many factors 720 has, first find its prime factorization: . All of its factors will be of
the form . Now there are five choices for a (a= 0, 1, 2, 3, or 4), three choices for b (b = 0, 1,
or 2), and two choices for c (c= 0 or 1). The total number of factors is therefore 5 x 3 x 2 = 30. 720 has 30
Greatest Common Factor/Divisor
The easiest way to find
the GCF is to take the prime factorization and multiply all of the primes that appear in both numbers. So
since 56 = 2 x 2 x 2 x 7 and 70 = 2 x 5 x 7, the GCF is 2 x 7 = 14. If two numbers share no primes, the GCF is 1.
Least Common Multiple
To find the LCM of any
two numbers, take the prime factorization of each number, find what prime factors appear in both, and
multiply one of each of the shared primes and then by all the unshared primes. So for example, 12 = 2 x 2 x
3, and 56 = 2 x 2 x 2 x 7, so the LCM of 12 and 56 is (2 x 2) [shared primes] x 3 [12's unshared primes] x (2*7)
[56's unshared primes] = 168. The largest possible LCM for any two numbers is one multiplied by the other.
3 : sum of digits divisible by 3
4 : the last two digits of number are divisible by 4
5 : the last digit is either a 5 or zero
6 : even number and sum of digits is divisible by 3
8 : if the last three digits are divisible by 8
9: sum of digits is divisible by 9
% change = change/original value
Fractions as exponents
x ^ 1/2 = √ x. x ^ 2/3 = 3√ of x ^2
√20 = √5
5*2*2 = 2√5
2√5 + 3√5 = 5√5
2/5 x = 8. --> multiply both sides by inverse, 5/2. 5/2(8) = 40/2 = 20
The inequality's direction changes when multiplied or divided by a negative number.
Reverse steps inequalities
If |x| < 3, then -3 < x < 3; if |x| > 3, then x > 3 or x < -3.
Total degrees of polygons
180 (n-2) , n = number of sides
Area of Triangle
Isosceles Triangle Properties
An isosceles right triangle (45-45-90) has sides in a ratio of x : x : x√2
sides in a ratio of x:x√3:2x, with the 1x side opposite the 30 degree angle
Angle of Triangle in relation to side length
Any given angle of a triangle corresponds to the length of the opposite side. The larger the degree measure
of the angle, the larger the length of the opposite side.
Sides of triangles that work out as exact integers. 3-4-5, 5-12-13, 8-15-17, 7-24-25. A multiple of a Pythagorean triple is a Pythagorean triple (e.g., 6-8-10).
Properties of Circle
Part of the circumference, measured in degrees out of 360, in relation to the central angle.
Arc = x/360 (πD)
a chunk of the circle. A = x/360 (πr^2) (where x is number of degrees in central angle)
Inscribed angle - circles
Inscribed angles that have a chord of the same length are equal
Diagonals of a rhombus
The diagonals of a rhombus bisect one another, forming four 90 degree angles
V = s^3
Surface Area = 6s^2
V = Height x Depth x Width
SA = 2(HxD) + 2(HxW) + 2(D+W)
V = r^2 (pi)(h)
SA = A=2πrh+2πr^2
When given two points and need to find equation of line ****
1) find the slope using the above formula
2) plug one of the points into y = mx+b and solve for b
Slope of two lines perpendicular
in the ratio of x : -1/x, where x is the
slope of one of the lines (think: negative reciprocal).
Distance formula for points
Work Rate formula
1 / Avg. Work Rate = 1 / Work Rate1 + 1/ Work Rate 2
where P is principal, r is rate, and t is time
where n is the number of times compounded per year
(proportion) x (group A average) + (proportion) x (group B average) + ...
Standard Deviation ***
1 m^2 = (100 cm)^2 = 10,000 cm^2
1 sq ft = 1 ft^2 = (12 inches)^2 = 144 sq inches