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Wednesday 7th of December
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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Finding Factors

Examples with Solutions

EXAMPLE 1

What are the factors of 45?

Solution

Let’s see if 45 is divisible by 1, 2, 3, and so on, using the divisibility tests wherever they apply.

 Is 45 divisible by Answer 1? Yes, because 1 is a factor of any number; , so 45 is also a factor. 2? No, because the ones digit is not even. 3? Yes, because the sum of the digits, 4 + 5 = 9, is divisible by 3; , so 15 is also a factor. 4? No, because 4 will not divide into 45 evenly. 5? Yes, because the ones digit is 5; , so 9 is also a factor. 6? No, because 45 is not even. 7? No, because 45 Ã· 7 has remainder 3. 8? No, because 45 Ã· 8 has remainder 5. 9? We already know that 9 is a factor.

The factors of 45 are therefore 1, 3, 5, 9, 15, and 45.

Note that we really didn’t have to check to see if 9 was a factor—we learned that itwas when we checked for divisibility by 5. Also, because the factors were beginning torepeat with 9, there was no need to check numbers greater than 9.

EXAMPLE 2

Identify all the factors of 60.

Solution

Let’s check to see if 60 is divisible by 1, 2, 3, 4, and so on.

 Is 60 divisible by Answer 1? Yes, because 1 is a factor of all numbers; , so 60 is also a factor. 2? Yes, because the ones digit is even; , so 30 is also a factor. 3? Yes, because the sum of the digits, 6 + 0 = 6, is divisible by 3; , so 20 is also a factor. 4? Yes, because 4 will divide into 60 evenly; , so 15 is also a factor. 5? Yes, because the ones digit is 0; , so 12 is also a factor. 6? Yes, because the ones digit is even and the sum of the digits is divisibleby 3; , so 10 is also a factor. 7? No, because 60 Ã· 7 has remainder 4. 8? No, because 60 Ã· 8 has remainder 4. 9? No, because the sum of the digits, 6 + 0 = 6, is not divisible by 9. 10? We already know that 10 is a factor.

The factors of 60 are therefore 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Can you explain how we knew that 10 was a factor of 60 when we checked for divisibility by 6?

EXAMPLE 3

A presidential election takes place in the United States every year thatis a multiple of 4. Was there a presidential election in 1866?

Solution

The question is: Does 4 divide into 1866 evenly? Using the divisibility test for 4, we check whether 66 is a multiple of 4.

Because has remainder 2, 4 is not a factor of 1866. So there was nopresidential election in 1866.