5.1 Prime and Composite Numbers

Prime Number

A natural number greater than 1 that has only itself and 1 as factors. OR A natural number that has exactly two different natural number factors.

Composite Number

A natural number greater than 1 that is NOT prime.

Factor

A number that is multiplied by another number to get a product

Multiple

A product of a given whole number and any other whole number.

Factorization

A representation of an expression as a product of two or more expressions

Sieve of Eratosthenes

Algorithm for finding prime numbers named for a Greek mathematician

Divisibility Tests

An aid to determine whether a natural number is divisible by another natural number.

Divisible (informal definition)

Can be divided by a number without leaving a remainder

Fundamental Theorem of Arithmetic

Every natural number can be factored into a unique product of primes

Divisibility Test for 8

Last three digits form a number divisible by 8

Divisibility Test for 4

Last two digits form a number divisible by 4

Divisibility Test for 10

The last digit is 0

Divisible (formal definition)

The natural number a is divisible by the natural number b if there exists a natural number k such that a = bk. If b divides a, then we write b | a.

Divisor

The number by which another number is divided.

Divisibility Test for 5

The number ends in a 0 or 5

Divisibility Test for 2

The number ends in a 0, 2, 4, 6, or 8

Divisibility Test for 6

The number is divisible by 2 and 3

Divisibility Test for 12

The number is divisible by 3 and 4.

Number Theory

The study of the properties of the natural numbers

Divisibility Test for 3

The sum of the digits is divisible by 3

Divisibility Test for 9

The sum of the digits is divisible by 9.

Natural Numbers

counting numbers OR positive integers