# Factoring & Multiples Worksheets

I find that there is a very underwhelming presence of this topic in the Common Core Curriculum. I think it is often overlooked, but the root of most algebra-based work is based on roots of factors and multiples. While their basic premise falls within the same territory, they are both very different things. Since they both involve the mathematical operation of multiplication, they often get confused. Factors are numbers that together form a product of another number. A single integer can have several different factors. A multiple is the end product of multiplying a number by an integer. Factors are fixed and as a result they are finite, multiples on the other hand are infinite because they just keep going. The topics that you will find on this page go in both directions and will give you a great deal of insight into the nature of this form of mathematics.

- Dilations and Scale Factors - This topic is applied to geometric shapes.
- Factor Pairs to 100 - We look at pairs of numbers that when multiplied give us the same product.
- Factors of an Integer - Many students think this is a brain storming activity, but it is far from it.
- Factoring by Grouping - We explore your more intermediate levels of skills.
- Greatest Common Factor and Least Common Multiple - This is starts with determine the prime factors between the values and seeing what they have in common.
- Missing Factors Multiplication - A great way to transition into Algebra.
- Multiplying by Multiples of 10 - The great old tens group gets pumped up in this section for sure.
- Prime and Composite Numbers - This is all determined by factors that exist within the values.
- Prime Factorization and Factor Trees - This comes down to breaking things down into smaller parts.
- Solve One-Variable Equations and Inequalities - Factors play a huge role in this section.
- Solving Linear Equations and Inequalities in One Variable - These can be used to work on higher level problems that you may encounter.
- Solving Quadratic Equations By Factoring - Start by checking for common factors. Then rewrite the problems with those factors in mind. From there it is usually simple operations and combining like terms.
- Using Division to Find Unknown Factors - We reverse the operations to find where the values will go.

### What are Factors?

Numbers that we multiply to get another name are known as factors of the answered number. Let's say that if you increase 2 and 3, the answer is 6, i.e., 2 and 3 are the factor of 6. However, factors are a concept that can be used in various other mathematical topics. Given that it is extensively part of algebra where one expression is divided by the other to find the factors.

Nonetheless, it is first necessary to learn the basics of factors before moving on to the advanced level. Let us take a few examples.

Find out the factors of 12. 12 can be obtained from multiplying 2 and 6, 3 and 4 and 12 and 1. So the factors of 12 are 1, 2, 3, 4, 6, 12.

Another number is 10. 10 can be obtained by multiplying 2 and 5 and by 10 and 1. Therefore, the factors of 10 are 1, 2, 5, 10. This is a huge skill to have and the fundamental skill in algebra.

### What are Multiples?

Multiples are values that you get when you multiply one whole number by another. It is the end product between two known values. The multiplication times tables are a list of a whole bunch of these. Every number is a multiple of itself and then they continue on infinitely. Any multiple of a value is greater than or equal to the number itself. 0 is a multiple of every number.

For example, the multiples of 4 are: 4, 8 ,12, 16, 20, 24, 28, 32, 36, 40… This can continue on infinitely always increasing by 4. If it is stated that a value is multiple of another number that also indicates that it can be divided by that value, it is a factor of. As we advanced on, we will learn about identifying multiples that two distinct values share.

### Similarities and Differences of Factors and Multiples

As we can see there is a good bit of crossover between these two. They do go off in separate directions because of the mathematical operations that are inherent to them. They are both related to opposite mathematical operations. Factors are found through division and multiples through multiplication. Factors are finite meaning that they are limited. Multiples are infinite meaning they are endless. When we determine a factor, it should be less than or equal to the number we are given. When we determine a multiply it should be greater than or equal to the given number.