Discrete Mathematics Flashcards

Flashcards covering divisibility, prime and composite numbers, LCM/GCF, and number systems.

Number Theory

A branch of mathematics concerned with integers and their properties.

Divisibility

Dividing a number evenly, with no remainder.

d | n

d divides n if there is no remainder on the division.

d ∤ n

d does not divide n.

Divisibility Rule for 2

If the last digit of the number is even (0, 2, 4, 6, or 8).

Divisibility Rule for 3

If the sum of the digits is divisible by 3.

Divisibility Rule for 4

If the number formed by the last two digits is divisible by 4.

Divisibility Rule for 5

If the last digit is either 0 or 5.

Divisibility Rule for 6

If it is divisible by both 2 and 3.

Divisibility Rule for 7

Take the last digit, double it, and subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven.

Divisibility Rule for 8

If the number formed by the last three digits is divisible by 8.

Divisibility Rule for 9

If the sum of the digits is divisible by 9.

Divisibility Rule for 10

If the last digit is 0.

Divisibility Rule for 11

If the difference between the sum of one set of alternate digits (from left to right) and the sum of the other set of alternate digits (from left to right) is 0 or divisible by 11.

Divisibility Rule for 12

If the number is divisible by both 3 and 4.

Prime Numbers

Positive integers greater than 1 that cannot be divided by any number except themselves and 1.

Composite Numbers

Positive integers that are greater than 1 and are not prime. A composite number can be divided by at least one number (a factor) other than itself.

Greatest Common Factor (GCF)

The largest non-zero integer d that is a common divisor of all the given integers.

Least Common Multiple (LCM)

The smallest integer that is a common multiple of all the given integers.

Prime Factorization

A way of expressing a number as a product of its prime factors.

Theorem for Number Systems

Expressing a positive integer uniquely in the form: n = amkm + am-1km-1 + … + a1k + a0

Decimal Number System

k = 10, digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Binary Number System

k = 2, digits: {0, 1}

Octal Number System

k = 8, digits: {0, 1, 2, 3, 4, 5, 6, 7}

Hexadecimal Number System

k = 16, digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}