# Simple Math Factoring Activities for All Ages

These simple math factoring activities for all ages are a fun way to practice math skills in your homeschool. You can play these with your children all together during Morning Time or you can work individually with kids to help them understand.

**Factoring Basics **

Before we begin factoring, let’s define what we mean by using this word. What is a factor?

**A factor is a number that divides a number exactly with no remainder. **

Factoring is the opposite of multiplying to find a product. Instead, it is starting with a product and finding the numbers that can be multiplied to make that product.

Why should students learn how to factor numbers? Factors are useful in reducing fractions. They are also an essential skill in solving quadratic trinomials which are usually introduced in high school Algebra classes.

Before students are ready to factor, they need to have plenty of mental math practice with multiplication facts. Whether you use flashcards, skip counting, or another math method, aim for your child to have the capability to answer multiplication problems automatically.

**Multiplication Chart**

One fun way to find factors is to use a multiplication chart. They won’t be able to find all the factors of a number this way, but it will be a great introduction to factoring.

Start with an easy number like 24. Have them circle all the 24s on the multiplication table. Next, have them highlight the corresponding rows and columns to find the factors of 24.

You can find a blank multiplication chart to print out and use here.

**Finding Factors Through Arrays**

One of the true methods that will help your child understand factors is to see them visually. For this number activity, you can use any simple math manipulative such as square tiles, cubes, playing cards, or even food like Cheerios.

I like to use square tiles. Give your child a certain number of tiles. Twelve is a good starting number. Tell your child to make rectangles with them. After they make a few different-sized rectangles, have them tell the dimensions by sides.

1×12

2×6

3×4

Tell your kids to write out the numbers of the sides like this. 1, 2, 3, 4, 6, and 12. Explain that these are factors.

Ask these questions.

Is 5 a factor of 12?

Is 7 a factor of 12?

After using the number 12, try giving them tiles with other numbers such as 20, 24, 32, 36, 40, 42, 48, 60, and 72.

You can extend this fun activity by having them draw arrays. Coloring them on graph paper is also fun!

**Loop Around Factoring Method**

My favorite factoring activity is what I call the Loop Around Method. This strategy will help a child find every factor of a product without any missing factors.

Begin with a number that has several factors. I like to use the number 24. Start with number 1 and go up.

Can 2 be multiplied evenly into 24?

What about 4?

Does 5 go evenly?

When you get to 6 which is already on the other side (4×6), you have “looped around.” Now you have listed all the proper factors. The rest of the factors go up until you hit 24 at the top.

Next, I list the factors below to help them visually see all the factors of 24.

When I teach this to my kids, I like to give them one or two types of problems as warm-ups and then have them do a some as independent work for extra practice.

Play this fun game over and over again with numbers that have a handful of factors like 20, 30, 32, 36, 40, 42, 48, 60, 72.

**Common Factors**

Once kids can find and list all the factors of a number**,** it is easy to have them find common factors by grouping problems. Show the factors of two numbers side by side like this.

24- 1, 2, 3, 4, 6, 8, 12, 24

36- 1, 2, 3, 4, 6, 9, 12, 18, 36

Tell them to circle the common factors.

### Greatest Common Factor

To further give your students understanding, ask them to show the greatest of the common factors. (In the numbers 24 and 36, the greatest common factor is 12.)

Finding the Greatest Common Factor, or GCF, will help in factoring quadratic trimomials in algebra.

**Difference Between Factors and Multiples**

I also like to teach my kids the difference between factors and multiples. Unlike factors, multiples begin with small numbers that multiply themselves. The easiest way to understand them is to see that they are skip counting.

2-2,4,6,8,12…

3-3,6,9,12,15,18…

4-4,8,12,16,20,24…

**Finding Prime Numbers with Factor Trees**

Factor trees are an engaging way for kids to learn about prime and composite numbers.

A prime number is divisible by only 1 and itself. (1,3,5,7,11,13) A composite number is divisible by more numbers than one and itself. (2,4,6,8,9,12,14,15)

To make factor trees, start with an easy number to factor. Draw two branches below the number and write two numbers that can be multiplied together to make the number above. Keep making branches below the composite numbers until the only remaining numbers are prime.

*Important note! Not all factor trees look the same. There is more than one way to make a tree, depending on the factors you choose.

**Factoring Quadratic Polynomials**

For the most part, homeschool parents are ok with teaching subjects like social studies, general science, and physical education, but when it comes to all things algebra, this is a daunting task most prefer to avoid! Because they are not middle school or high school math teachers, parents become hesitant about anything involving a graphing calculator or words like “perfect square trinomials.”

Now I will be the first to admit that I think some higher-level math is not necessary for future life skills, but quadratic polynomial equations are kind of fun once you understand them. I like to think of quadratic expressions as factor puzzles. Basic multiplication and factoring are the main skills needed to perform them. If you like fun math games like Sudoku, you might be surprised to learn that you like to factor polynomials!

### Easy Trinomials

Let’s start with some easy trinomials like the one below.

X²+10x + 24

Seeing the **patterns** in these expressions is a new way to help you solve them more quickly. They usually begin with three terms and end with two parentheses expressions like below.

X² +10x + 24= (x+4)(x+6)

What is important to know is that the **second term represents the SUM** of two factors of a number and the **third term represents the PRODUCT **of those same two factors.

If you are familiar with the factors of 24, you can easily break down this trinomial.

Use the Loop Around Method above to write out the factors of 24. Ask these questions.

1.What two numbers multiplied together make 24, but added together make 14? (2×12)

2.Which two numbers multiplied together make 24, but added together make 11? (3×8)

3. What two numbers multiplied together make 24, but added together make 10? (4×6)

Since 10 is the 2nd term, it is easy to see that the factors 4 and 6 will be used in solving this trinomial.

### Step-by-Step

- Separate the first term by putting an x in the correct place (as the first term) in each parenthesis.
- Numbers 4 and 6 can be used as the second term in each parenthesis because added together they make 10 and multiplied together they make 24.

Use the FOIL Method to multiply it out and check.

Here is another product with some corresponding polynomials you can solve.

**32**

1×32

2×16

4×8

Ask these questions.

- Which two numbers multiplied together make 32, added together make 33? (1×32)
- What two numbers multiplied together mke 32, but added together make 18? (2×16)
- Find two numbers that multiplied together make 32, but added together make 12? (4×8)

X² + 18x + 32 Answer: (x+2)(x+16)

X² + 12x +32 Answer: (x+4)(x+8)

X² +33x +32 Answer (x+1)(x+32)

Now try these expressions. Start by looking at the third term and using the Loop Around Method to find all the factors first and then solve.

(Remember! 2nd Term= **sum**, 3rd Term = **product**)

X²+5x+6 Answer (x+2)(x+3)

X²+12x+27 Answer (x+9)(x+3)

X²+9x+20 Answer (x+5)(x+4)

X²+13x+40 Answer(x+8)(x+5)

X²+15x+56 Answer (x+7)(x+8)

Once you get the hang of it, you can try creating polynomials, grouping problems by the products and factors you find in the Loop Around Method.

You may not know anything about Algebra or quadratic equations, but you can still prepare your older children for the kinds of problem-solving that they will have to do in Algebra I and II by trying this simple game.

Your algebra students don’t need special classes to solve quadratic expressions. Although these types of problems do require a bit of good criminal investigation, with a lot of practice, your kids can solve them quickly!

## More Simple Factoring Activities

For more resource types like this, you can try these digital factoring options in which you compete with the computer playing digital factoring games.

You may also enjoy reading this similar post.

Five Minute Homeschool Math Games to Do With Everyone

Difference of Squares is an interesting puzzle to solve as well. You can find a good example in this video.

If you want to learn about the box method of solving quadratic polynomials, I like how this video explains it. This step gets a little more challenging because it involves negative terms.

Happy factoring everyone!