Algebra Tutorials!
Monday 15th of July
 Home Rotating a Parabola Multiplying Fractions Finding Factors Miscellaneous Equations Mixed Numbers and Improper Fractions Systems of Equations in Two Variables Literal Numbers Adding and Subtracting Polynomials Subtracting Integers Simplifying Complex Fractions Decimals and Fractions Multiplying Integers Logarithmic Functions Multiplying Monomials Mixed The Square of a Binomial Factoring Trinomials The Pythagorean Theorem Solving Radical Equations in One Variable Multiplying Binomials Using the FOIL Method Imaginary Numbers Solving Quadratic Equations Using the Quadratic Formula Solving Quadratic Equations Algebra Order of Operations Dividing Complex Numbers Polynomials The Appearance of a Polynomial Equation Standard Form of a Line Positive Integral Divisors Dividing Fractions Solving Linear Systems of Equations by Elimination Factoring Multiplying and Dividing Square Roots Functions and Graphs Dividing Polynomials Solving Rational Equations Numbers Use of Parentheses or Brackets (The Distributive Law) Multiplying and Dividing by Monomials Solving Quadratic Equations by Graphing Multiplying Decimals Use of Parentheses or Brackets (The Distributive Law) Simplifying Complex Fractions 1 Adding Fractions Simplifying Complex Fractions Solutions to Linear Equations in Two Variables Quadratic Expressions Completing Squares Dividing Radical Expressions Rise and Run Graphing Exponential Functions Multiplying by a Monomial The Cartesian Coordinate System Writing the Terms of a Polynomial in Descending Order Fractions Polynomials Quadratic Expressions Solving Inequalities Solving Rational Inequalities with a Sign Graph Solving Linear Equations Solving an Equation with Two Radical Terms Simplifying Rational Expressions Exponents Intercepts of a Line Completing the Square Order of Operations Factoring Trinomials Solving Linear Equations Solving Multi-Step Inequalities Solving Quadratic Equations Graphically and Algebraically Collecting Like Terms Solving Equations with Radicals and Exponents Percent of Change Powers of ten (Scientific Notation) Comparing Integers on a Number Line Solving Systems of Equations Using Substitution Factoring Out the Greatest Common Factor Families of Functions Monomial Factors Multiplying and Dividing Complex Numbers Properties of Exponents Multiplying Square Roots Radicals Adding or Subtracting Rational Expressions with Different Denominators Expressions with Variables as Exponents The Quadratic Formula Writing a Quadratic with Given Solutions Simplifying Square Roots Adding and Subtracting Square Roots Adding and Subtracting Rational Expressions Combining Like Radical Terms Solving Systems of Equations Using Substitution Dividing Polynomials Graphing Functions Product of a Sum and a Difference Solving First Degree Inequalities Solving Equations with Radicals and Exponents Roots and Powers Multiplying Numbers
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# 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.

 Copyrights © 2005-2024