152 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Section 2.2 Prime Numbers and Factorization Key Concepts A factorization of a number is a product of factors that equals the number. A number is divisible by another if their quotient leaves no remainder. Divisibility Rules for 2, 3, 5, and 10 • A whole number is divisible by 2 if the ones-place digit is 0, 2, 4, 6, or 8. • A whole number is divisible by 3 if the sum of the digits of the number is divisible by 3. • A whole number is divisible by 5 if the ones-place digit is 0 or 5. • A whole number is divisible by 10 if the ones-place digit is 0. A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. Composite numbers are whole numbers that have more than two factors.The numbers 0 and 1 are neither prime nor composite. Prime Factorization The prime factorization of a number is the factorization in which every factor is a prime number. A factor of a number n is any number that divides evenly into n. For example, the factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. Examples Example 1 and are two factorizations of 16. 4 4 8 2 Example 2 15 is divisible by 5 because 5 divides into 15 evenly. Example 3 382 is divisible by 2. 640 is divisible by 2, 5, and 10. 735 is divisible by 3 and 5. Example 4 9 is a composite number. 2 is a prime number. 1 is neither prime nor composite. Example 5 2)756 2)378 3)189 3)63 3)21 7 The prime factorization of 756 is 2 2 3 3 3 7 or 22 33 7
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