1.1 Factor (divisor): One of two or more whole numbers that are multiplied to get a product. For example, 1, 2, 3, 4, 6, and 12 are factors of 12 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 Factors are also called divisors since 12 1 = 12 and 12 12 = 1 12 2 = 6 and 12 6 = 2 12 4 = 3 and 12 3 = 4 Multiple : The product of a given whole number and another whole number. For example, some multiples of 3 are 3, 6, 9, and 12. Example- 12 is a multiple of 3 and 3 is a factor of 12. Proper factors : All the factors of a number except the number itself. For example, the proper factors of 16 are 1, 2, 4, and 8.
1.2 Prime Number : A number with exactly two factors, 1 and the number itself. Examples of primes are 2, 3, 5, 7, 11, 13, and 17. The number 1 is not a prime number because it only has one factor. Composite Number : A whole number with factors other than itself and 1 (so, a whole number that is not prime). Some composite numbers are 4, 6, 8, 9, 10, 12 1.4 Factor Pair : Two whole numbers that are multiplied to get a product. Examples- 13 and 4 are a factor pair because 13x4=52, 5 and 4 are a factor pair because 5x4=20 Square Number: A number that is a product of a number multiplied by itself. Example 3x3=9 Abundant Numbers: Abundant means more than enough, which is appropriate since the sum of an abundant number s proper factors is more than the number.example 12. The proper factors of 12 are 1, 2, 3, 4, 6, which total 16.
Deficient Numbers : Deficient means not enough, which is appropriate since the sum of a deficient number s proper factors is less than the number. Example: 15. The proper factors of 15 are 1, 3, and 5 which total 9. Perfect Numbers : Perfect means exactly right, which is appropriate because the sum of a perfect number s proper factors is equal to the number. Example: 6. The proper factors of 6 are 1, 2, and 3 which total 6. 2.1 Common Multiple : A multiple that 2 or more numbers share. Example- the first few multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40. The first few multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. From these lists, we can see that two common multiples of 5 and 3 are 15 and 30. Least Common Multiple (LCM): The least multiple (the smallest multiple) that two or more numbers share. Common multiples of 3 and 5 are 15, 30, and 45. The least common multiple of 3 and 5 is 15. Common Factors : A factor that two or more numbers share. Example- 7 is a common factor of 14 and 35 because 7 is a factor of 14 (7x2=14) and 7 is a factor of 35 (7x5=35)
Greatest Common Factor (GCF): The greatest factor that two or more numbers share. For example, 1, 2, 3, and 6 are common factors of 12 and 30, but 6 is the greatest (or biggest) factor. 2.2 Counter Example: An example that disproves a statement 3.2 Factorization : A string of factors for a given product. A product can have many factorizations. Example: two factorizations for 60 are 3 x 20 and 2 x 2 x 15. Prime Factorization : A string of prime numbers, perhaps with some repetitions, resulting in a desired product. Example: The prime factorization of 540 is 5 x 3 x 3 x 3 x 2 x 2 Exponent : The small raised number that tells how many times a factor is used. Example: 5 3 means 5 x 5 x 5. The exponent is 3. 3.3
Relatively Prime: A pair of numbers with no common factors other than 1. Example: 20 and 33 are relatively prime because the factors of 20 are 1, 2, 4, 5, 10 and 20 and the factors of 33 are 1, 3, 11 and 33. Notice that neither 20 nor 33 is a prime number itself. 4.1 Numerical expression: A numerical expression represents a single value. It consists of one or more numbers and operations. Example: 5+1 is a numerical expression representing 6. Numerical expressions can be used as a factor. Example: 12 = 2 (5+1). This example shows the product of 2 and the expression 5+1. Equivalent expressions: Expressions that represent the same quantity. Example: 2+5 and 3+4 are equivalent expressions Conjecture: A claim (your best guess) about a pattern or relationship based on observations. Distributive Property: A mathematical property that connects the operations of addition and multiplication. For any 3 numbers, a, b, and c, a ( b + c )= ab + ac
Example: 2 (3+5) = 2(3) + 2(5) Factored Form: a(b+c) Expanded Form: a(b) + a(c)