Discrete Math - EXAM 3 (Lessons 14,15, & 16)

Spring 2025 / EZZ ASFFF DISCRETE GOAT

Divisibility Formula

b = a(c), b not being 0, and all being ints

Quotient Formula

⌊(a/d)⌋ - a div d

Remainder Formula

a - d(q) - a mod d

a ≡ b (mod m) IAOI…

a mod m ≡ b mod m (same remainder)

Base 10 Expansion

Decimal Expansion

Base 2 Expansion

Binary Expansion

Base 16 Expansion

Hexadecimal Expansion

Hexadecimal A,B,C,D,E,F Respectively

10,11,12,13,14,15

Expansion from any other base to base 10

super easy one

expanding any base 10 number to anything else

div and mod,

converting binary to hexadecimal

divide into 4 and then so the easy method

n is said to be prime if…

only positive factors of n are 1 and n

n is said to be composite if…

it is not prime / IS composed of other primes

life hack to testing if a number is prime

take the value of the square root of that number, and test the original value by all primes below the new value you got

First 30 Primes (recite them)

2,3,5,7,11,13,17,19,23,29

The Fundamental Theorem of Arithmetic

AKA Prime Factorization, try 2’s, 3’s, 5’s, 7’s, etc.

Greatest Common Divisor

The biggest number that fits into both numbers

Lowest Common Multiple

Smallest multiples two numbers have in common when added by themself

Relatively Prime

gcd(a,b) = 1