Factors/Multiples/Prime/Composite
Multiple
1. The numbers you say when you count by that number. 2. A product that be reached by multiplying that number by another whole number.
How can we use this: "If pⁿ is a prime number to the nth power, how many factors does it have" To answer this?: How many factors does 72 have?
72 = 2×2×2×3×3 = 2³×3². Since 2³ has 4 factors and 3² has 3 factors, 72 has 4×3 = 12 factors. The factors may be obtained by multiplying any one of the factors of 2³ by any one of the factors of 3²: (1, 2, 2², 2³) × (1, 3, 3²). Written in order in standard form, the 12 factors are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Composite number
A counting number which has at least three different factors, namely the number itself, the number 1, and at least one other factor.
Prime number
A counting number which has exactly two different factors, namely the number itself and the number 1
Factor (factor pairs)
A number, a, is said to be a factor of a number, b, if ac=b. That is, if a can be multiplied with another factor to equal b.
Fundamental theorem of arithmetic
All counting numbers greater than one are either prime or they are the product of a unique combination of prime factors.
Relatively prime or co-prime.
If the GCF of two numbers is 1.
What is the greatest common factor of two natural numbers times the least common of those two natural numbers equal to?
It is equal to the product of those natural numbers. or GCF (A,B) x LCM (A,B) = A x B For example, GCF (9,12) x (LCM (9,12) = 3 x 36 = 108 and 9 x 12 = 108
Is the number 1 prime or composite?
It is neither prime nor composite since it has exactly one factor, namely the number itself. Thus, there are 3 separate categories of counting numbers: prime, composite, and the number 1.
What theorem can be used to find the greatest common factor of any two natural numbers?
The greatest common factor (GCF) of any two natural numbers can be found by evaluating the following quotient: (A x B)/LCM (A,B) That is, the product of the two natural numbers divided by the least common multiple of the same two natural numbers.
Greatest Common Factor (GCF)
The largest counting number that divides each of the two given numbers with zero remainder. Example: GCF(12,18) = 6.
What theorem can be used to find the least common multiple of any two natural numbers?
The least common multiple (LCM) of any two natural numbers can be found by evaluating the following quotient: (A x B)/GCF (A,B) That is, the product of the two natural numbers divided by greatest common factor of the same two natural numbers.
Least Common Multiple (LCM)
The smallest counting number that each of the given numbers divides with zero remainder. Example: LCM (12,18) = 36.
How many prime numbers are there between 1 and 100 and what are they?
There are twenty-five prime numbers between 1 and 100. They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. (Memorize the I'm prime song on youtube).
factored completely
When a number is expressed as a product of only prime numbers. Example: 144 = 2×2×2×2×3×3.
If pⁿ is a prime number to the nth power, how many factors does it have.
n+1 factors Example: 2×2×2×2×2 = 2⁵ has 6 factors which are 1, 2, 2×2, 2×2×2, 2×2×2×2, 2×2×2×2×2. In exponential form, the factors are: 1, 2, 2², 2³, 2⁴, and 2⁵. In standard form, the factors are: 1, 2, 4, 8, 16, and 32. Notice that the factors of 2⁵ include both 1 and 2⁵