Number Properties Flashcards
Divisibility/Primes
- “x is div by y” “x is a mult of y” “y is a factor of x” “x/y is an integer”
all mean: “x has at least the primes that are in y.”
“prime factors of 12” (2 * 2 * 3) vs. “factors/divisors of 12” (1, 2, 3, 4, 6, 12)
LCM of X and Y = Smallest number that has minimum primes of X and Y.
GCF of X and Y = the primes that X and Y have in common.
for any number: [mult of x] + / – [mult of x] = mult of x
f.e. (26x + 65) is a multiple of 13, because 26x and 65 are multiples of 13
[RARE: To calculate how many factors a number would have, you add 1 to
all the exponents of its prime factorization and multiply them. 600 = 2^3 * 3^1 * 5^2 –> (3+1)(1+1)(2+1) = 4 * 2 * 3 = 24 factors]
Odds / Evens
E +/- E = E E * E = E
E +/- O = O E * O = E
O +/- O = E O * O = O
(biggest thing: even * anything = even)
3x + 4y is odd –> 3x + E = O —> 3x = O —> x = O
12x + 5y is even –> E + 5y = E - –> 5y = E –> y = E
Positives / Negatives
x+y > 0 (at least one pos)
x+y < 0 (at least one neg)
x-y > 0 (x > y)
x-y < 0 (x < y)
xy > 0 or x/y > 0 (same sign)
xy < 0 or x/y < 0 (opposite signs)
“x/y is even” -> “x/y = E” -> “x = E * y” -> x is even, y is ??
“x/y is odd” -> “x/y = O” -> “x = O * y” -> both even or both odd
raised to an even power, sign is hidden (given: x^2 > 0, x could be pos or neg)
raised to an odd power, sign is visible
(if x^3 > 0, then x > 0. if x^3 < 0, then x < 0)
Probability
