"A composite number is a positive integer that can be formed by multiplying two smaller positive integers."
Numbers that can be divided by more than two numbers.
Prime numbers: Prime numbers are positive integers that are divisible only by 1 and themselves.
Divisibility rules: Divisibility rules are rules that help determine whether a number is divisible by another number.
Multiples: Multiples are the result of multiplying a number by an integer.
Factors: Factors are numbers that divide into another number without leaving a remainder.
Greatest Common Factor (GCF): The GCF is the largest factor that is common to a set of numbers.
Least Common Multiple (LCM): The LCM is the smallest multiple that is common to a set of numbers.
Euclidean algorithm: The Euclidean algorithm is a method for finding the GCF of two numbers.
Fundamental Theorem of Arithmetic: The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be expressed as a unique product of prime numbers.
Sieve of Eratosthenes: The Sieve of Eratosthenes is a method for finding all prime numbers up to a given limit.
Composite numbers: Composite numbers are positive integers that are not prime.
Square Numbers: Square numbers are numbers that are the product of an integer multiplied by itself.
Cube Numbers: Cube numbers are numbers that are the product of an integer multiplied by itself twice.
Rational Numbers: Rational numbers are numbers that can be expressed as a ratio of two integers.
Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a ratio of two integers.
Real Numbers: Real numbers are all the numbers on the number line.
Imaginary Numbers: Imaginary numbers are numbers that cannot be expressed as real numbers.
Perfect Numbers: Perfect numbers are numbers that are equal to the sum of their proper divisors.
Amicable Numbers: Amicable numbers are two numbers that are each equal to the sum of the proper divisors of the other.
Abundant Numbers: Abundant numbers are numbers whose proper divisors sum to a value greater than the number itself.
Deficient Numbers: Deficient numbers are numbers whose proper divisors sum to a value less than the number itself.
Abundant numbers: These are composite numbers where the sum of their proper divisors is greater than the number itself.
Deficient numbers: These are composite numbers where the sum of their proper divisors is less than the number itself.
Semiperfect numbers: These are composite numbers that are equal to the sum of some or all of their proper divisors.
Powerful numbers: These are composite numbers where each prime factor occurs at least twice in the factorization.
Smith numbers: These are composite numbers where the sum of their digits is equal to the sum of the digits in the factorization of its prime factors.
Pseudoperfect numbers: These are composite numbers that are very similar in nature to semiperfect numbers but not all of their proper divisors are used.
Sphenic numbers: These are composite numbers that are the product of exactly three distinct primes.
Composites distinct from their prime factors: These are composite numbers that cannot be expressed as the product of only one prime.
Carmichael numbers: These are composite numbers that satisfy a congruence condition that makes them look like prime numbers.
"The composite numbers are exactly the numbers that are not prime."
"Every positive integer is composite, prime, or the unit 1."
"For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7."
"The integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself."
"The composite numbers up to 150 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32..."
"Every composite number can be written as the product of two or more (not necessarily distinct) primes."
"Furthermore, this representation is unique up to the order of the factors."
"This fact is called the fundamental theorem of arithmetic."
"There are several known primality tests that can determine whether a number is prime or composite."
"...without necessarily revealing the factorization of a composite input."
"It is a positive integer that has at least one divisor other than 1 and itself."
"This representation is unique up to the order of the factors."
"...the composite number 299 can be written as 13 × 23."
"...the composite number 360 can be written as 23 × 32 × 5."
"...the composite numbers up to 150 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38..."
"Every positive integer is composite, prime, or the unit 1."
"It is a positive integer that has at least one divisor other than 1 and itself."
"This representation is unique up to the order of the factors."
"There are several known primality tests that can determine whether a number is prime or composite, without necessarily revealing the factorization of a composite input."