**Elementary
Algebra Exercises Section 1.2**

**17.** To find the factors of 20, test all numbers less than or equal to the square root of 20.

If a number is a factor then the corresponding quotient is also a factor.

1 is a factor and so is the quotient 20

2 is a factor and so is the quotient 10

3 is not a factor

4 is a factor and so is the quotient 5

Because 5^{2} is larger than 20 we do not need to test any other numbers.

The factors of 20 are, 1, 2, 4, 5, 10, and 20.

**18.** To find the factors of 50 we test all numbers less than or equal to the square root of 50.

If a number is a factor then the corresponding quotient is also a factor.

1 is a factor and so is the quotient 50

2 is a factor and so is the quotient 25

3 is not a factor

4 is not a factor

5 is a factor and so is the quotient 10

6 is not a factor

7 is not a factor

Because 8^{2} is larger than 50 we do not need to test any other numbers.

The factors of 50 are 1, 2, 5, 10, 25, and 50

**19.** To find the factors of 28 we test all numbers less than or equal to the square root of 28.

If a number is a factor then the corresponding quotient is also a factor.

1 is a factor and so is the quotient 28

2 is a factor and so is the quotient 14

3 is not a factor

4 is a factor and so is the quotient 7

5 is not a factor
Because 6^{2} is larger than 28 we do not need to test any other numbers.

The factors of 28 are 1, 2, 4, 7, 14, and 28

**20.** To find the factors of 36 we test all numbers less than or equal to the square root of 36.

If a number is a factor then the corresponding quotient is also a factor.

1 is a factor and so is the quotient 36

2 is a factor and so is the quotient 18

3 is not a factor

4 is a factor and so is the quotient 9

5 is not a factor

6 is a factor and so is the quotient 6, but we already know that.

Because 6^{2} is equal to 36 we do not need to test any other numbers.

The factors of 36 are 1, 2, 4, 6, 9, 18, and 36

The prime factorization of 75 is (3)(5)(5). Therefore 75 = (3)(5)(5) and If we use exponents 75 = (3)5 ^{2} |
22. Find the prime factorization of 20.The prime factorization of 20 is (2)(2)(5). Therefore 20 = (2)(2)(5) and if we use exponents 20 = 2 ^{2}5 |

23. Find the prime factorization of 28.The prime factorization of 28 is (2)(2)(7) Therefore 28 = (2)(2)(7) If we use exponents 28 = 2 ^{2}7 |
24. Find the prime factorization of 54.The prime factorization of 54 is (2)(3)(3)(3) Therefore 54 = (2)(3)(3)(3) If we use exponents 54 = (2)3 ^{3} |

25. Find the prime factorization of 117.The prime factorization of 117 is (3)(3)(13) Therefore 117 = (3)(3)(13) If we use exponents 117 = 3 ^{2}13 |
26. Find the prime factorization of 147.The prime factorization of 147 is (3)(7)(7) Therefore 147 = (3)(7)(7) If we use exponents 147 = (3)7 ^{2} |

27. Find the prime factorization of 220.The prime factorization of 220 is (2)(2)(5)(11) Therefore 220 = (2)(2)(5)(11) If we use exponents 220 = 2 ^{2}(5)(11) |
28. Find the prime factorization of 270.The prime factorization of 270 is (2)(3)(3)(3)(5) Therefore 270 = (2)(3)(3)(3)(5) If we use exponents 270 = (2)(3 ^{3})(5) |