The counting numbers or natural numbers are the same as the whole numbers, except they do not include zero.,

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1 Factors, Divisibility, and Exponential Notation Terminology The whole numbers start with zero and continue infinitely., The counting numbers or natural numbers are the same as the whole numbers, except they do not include zero., Factors are numbers multiplied together. The result of the multiplication is called the product. To find all the factors of a number, divide by the counting numbers { If you get a remainder, then the number is not a factor. Stop when you get factors that have already been listed., }. Example 1 Find all the factors of. is not divisible by is not divisible by is not divisible by. We already have these factors. This means we are done. We have found all possible factors. the factors of 60 are. Prime Number A Prime number is a counting number greater than 1 that has exactly two different factors, itself and one. The set of prime numbers are infinite. The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, Notice the prime numbers have exactly two factors. The number itself and. Composite Number A Composite number is a counting number greater than 1 that is not a prime number. The set of composite numbers are infinite. Composite numbers are:, Page 1 of 7

2 Neither Prime nor Composite 0 and 1 are neither prime nor composite. Labeling a Number as Prime or Composite Find all the factors of a number. A prime number will have exactly two factors, itself and one. Otherwise Example 2 Is a prime or composite number? List all factors of 7. All factors of : Since has exactly two different factors, it is a prime number. Prime Example 3 Is 25 a prime or composite number? List all factors of. All factors of : Since 25 has more than two different factors, Composite Example 4 Is a prime number or a composite number? List all factors of All factors of : Since 50 has more than two different factors, Composite Example 5 Is a prime number or a composite number? List all factors of. All factors of : Since has exactly two different factors, it is a prime number. Prime Page 2 of 7

3 Example List all factors of All factors of : Since 91 has more than two different factors, it is a composite. Composite Example List all factors of All factors of : Since has more than two different factors, Composite Example List all factors of All factors of : Since has more than two different factors, Composite Example List all factors of All factors of : Since has more than two different factors, Composite Page 3 of 7

4 Exponential Notation Exponential notation represents repeated multiplication of a base number. a is called the base and is called the exponent. The expression can be read to the power. can be read to the second power or squared. can be read to the third power or cubed. can be read to the fourth power. Example 10 This can be read 3 to the fourth power. Example 11 This can be read 5 to the second power or 5 squared. Example 12 This can be read 2 to the third power or 2 cubed. Example 13 This can be read 2 to the first power. 2 Example 14 This can be read 7 to the second power or 7 squared. Page 4 of 7

5 MAT 040: Basic Math Example 15 This can be read a 4 to the second power or 4 squared. Example 16 This can be read as 3 to the third power or 3 cubed. Zero Power Any number to the zero power equals 1. Example 17 Find the product of Divisibility One number is divisible by another if when dividing the remainder is 0. Divisible by 2 A number is divisible by 2 if it ends in an even number such as 0, 2, 4, 6 or 8. Example 18 Which of the following numbers are divisible by 2? 48, 53 and 30 48: Yes 53: No, numbers divisible by 2 end in 0, 2, 4, 6, or 8. 30: Yes Page 5 of 7

6 Divisible by 3 A number is divisible by 3 if the sum of its digits is divisible by 3. Example 19 Which of the following numbers are divisible by 3? 187, 981, 111 and : No since 16 is not divisible by : Yes since 18 is divisible by : Yes since 3 is divisible by : No since 23 is not divisible by 3. Divisible by 5 A number is divisible by 5 if it ends in a 0 or 5. Example 20 Which of the following numbers are divisible by 5? 538, 600 and : No since it ends in : Yes since it ends in : Yes since it ends in 5. Divisible by 10 A number is divisible by 10 if it ends in a 0. Page 6 of 7

7 Example 21 Which of the following numbers are divisible by 10? 7345, 600, 1309 and : No since it ends in : Yes since it ends in : No since it ends in : Yes since it ends in 0. Brenda Moore and Indian Hills Community College Page 7 of 7

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