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
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
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.