Lesson Video: Factors Using Models Mathematics • 4th Grade

In this video, we will learn how to find positive factors of whole numbers using models.

08:04

Video Transcript

Factors: Using Models

In this video, we’re going to learn how to find positive factors of whole numbers using models. Factors are numbers we multiply together to make a product. Two multiplied by five is 10. So we can say that two and five are factors of 10. 10 is the product of two and five. What do you think the factors of the number one are? Which two numbers could we multiply together to give us a product of one? One times one equals one. One is a factor of one. In fact, one is the only number which has one factor.

All the other numbers have at least two factors. So the number two has two factors. If one times two is two, we know that one and two are factors of two. Two is an even number. And we know that we can divide even numbers by two, and there’ll be no remainder. So if we were to divide our two grasshoppers into two equal groups, each group would contain one grasshopper, and there’ll be none left over.

So we know that even numbers will always have two as one of its factors. We know that four is also an even number. So we know that we can divide our four grasshoppers into two equal groups. Each of our two groups contains two grasshoppers. So we can say that two is a factor of four.

What are the factors of the number eight? Which numbers can we multiply together to give us a product of eight? Well, we’ve got a row of eight grasshoppers, which we can model using eight counters. One lot of eight or one row of eight equals eight. And if one times eight equals eight, we can say that one and eight are factors of eight. We could also arrange our eight grasshoppers into two rows of four.

This model shows us two rows of four counters. Two multiplied by four equals eight. So two and four are also factors of eight. So we can say that one and eight are a factor pair because they are two numbers which we multiply together to make our product of eight. One and eight are a factor pair, and two and four are a factor pair. The factors of eight are one, two, four, and eight.

So far in this video, we’ve learned that factors are numbers which we multiply together to make a product. Let’s try answering some questions now where we can practice what we’ve learned.

Write the pair of factors of six that are shown by this array.

In this question, we have to find the pair of factors of the number six that are shown by this array. We can see that our six squares have been arranged into three rows of two. So we know that three multiplied by two equals six. So three and two are a factor pair of six. If we multiply three and two, the product is six.

When we write factors of a number, we usually start by writing the numbers in order from smallest to largest. So we would say two and three are factors of six. This is the pair of factors of six shown by the array.

Write the pair of factors of 15 that are shown by this model.

In this question, we have to find the pair of factors of the number 15 shown by this area model. In this model, our 15 squares have been drawn using a rectangle which measures five squares by three squares. So we know that five multiplied by three equals 15. We could also say that three multiplied by five equals 15. So the pair of factors, or the factor pair, is the numbers three and five. Three and five are two numbers which we can multiply together to give us a product of 15. So the pair of factors of 15 that are shown by this model are three and five. Three and five are factors of 15.

How many factor pairs does the number 12 have?

In this question, we have to work out how many factor pairs the number 12 has. Here are 12 cubes. We’ve placed them in one row of 12, and we know that one multiplied by 12 equals 12. So the numbers one and 12 are a factor pair which make 12. Let’s mark our factor pair on our number line. Can you think of any more factor pairs which we multiply together to give us a product of 12? We know that 12 is an even number. What do we multiply by two to get 12? We can arrange our 12 cubes into two rows of six. So two and six are a factor pair which make 12.

So far, we’ve found two factor pairs. Can we divide 12 by three? Yes, we can. We can make three rows of four. So three and four are a factor pair which make 12. We can’t multiply five by another factor to make 12 or seven or eight, nine, 10, or 11. We found three factor pairs which multiply together to give us a product of 12. So the number 12 has three factor pairs: one and 12, two and six, and three and four.

What have we learned in this video? We’ve learned how to find factors of whole numbers using models.

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