1. Factor A factor of an integer is any integer that divides the given integer with no remainder.

2. Prime Number A prime number is a natural number greater than one that has exactly two positive factors: one and itself.

3. Tell whether 237 is divisible by 2, 3, 4, 5, or 6. Exercise 3 3

4. Tell whether 245 is divisible by 2, 3, 4, 5, or 6. 5 5 Exercise

5. Tell whether 10,164 is divisible by 2, 3, 4, 5, or 6. 2, 3, 4, 6 Exercise

6. Tell whether 111,222 is divisible by 2, 3, 4, 5, or 6. 2, 3, 6 Exercise

7. State the divisibility test for 9. Does 9 divide the sum of the digits? Exercise

8. Fundamental Theorem of Arithmetic Every composite integer greater than one can be written as a product of prime factors in exactly one way (though the order of the factors may vary).

9. Write the prime factorization of 42. Example 1 42 = 2 3 7 42 2 21 2 3 7

10. Write the prime factorization of 126. 126 = 2 3 2 7 126 63 21 7 7 1 1 2 2 3 3 3 3 7 7 Example 2

11. Divide out all 2s, then 3s, then 5s, and so on until the quotient is prime.

12. Write the prime factorization of 90. Example 3

13. Find the number whose prime factorization is given. 24 2 3 x 3 Example

14. Find the number whose prime factorization is given. 42 2 x 3 x 7 Example

15. Find the number whose prime factorization is given. 245 5 x 7 2 Example

16. Find the number whose prime factorization is given. 900 2 2 x 3 2 x 5 2 Example

17. Write the prime factorization of the number. 2 x 3 2 x 7 126 Example

18. Write the prime factorization of the number. 7272 7272 49 Example

19. Write the prime factorization of the number. 5454 5454 625 Example

20. Write the prime factorization of the number. 13 2 169 Example

21. Write the prime factorization of the number. 2 3 × 5 2 200 Example

22. Write the prime factorization of the number. 3434 3434 81 Example

23. Solve the equation to find the missing prime factor. s = 3 273 = s 7 13 Exercise

24. Solve the equation to find the missing prime factor. n = 7 105 = 3 5 n Exercise

25. Solve the equation to find the missing prime factor. c = 11 418 = 2 c 19 Exercise

26. Solve the equation to find the missing prime factor. y = 17 935 = 5 11 y Exercise

27. Solve the equation to find the missing prime factor. t = 7 238 = 2 t 17 Exercise

28. Solve the equation to find the missing prime factor. y = 5 1,235 = y 13 19 Exercise