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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.

What are Factors?

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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.

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