1.10 Factors of a Number
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Math Basics > Unit 1 Number Sense > Lesson 1.10 Factors of a Number
Video Lesson
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In this lesson, we're going to look at understanding what factors are and then how we can find them. So, factors are based on division. If we look at this division problem here, we see that we have 36 divided by four equals nine, and it's set up as long division problem. The 36 we call the dividend. The number we're dividing by the four in this case is the divisor. And then the answer that we get, nine, we call the quotient. Now notice with this division problem, there is no remainder. The quotient is just the whole number nine with no remainder. When there is no remainder, the divisor and the quotient are factors of the dividend. So another way of saying that is that we can divide four into 36 with no remainder and we can divide nine into 36 as well without having a remainder left over. We can classify numbers based on how many factors they have. Prime numbers have only two factors, the number one and the number itself. So for any type of number, they'll have at least those two numbers as factors, the number one and itself. Composite numbers are numbers that are not prime. So that means that they have more than two factors. So let's look at some examples. First, we have the number two. The number two has only two factors, one and itself, the number two. There are no other numbers that you can divide into the number two without having a remainder left over. So we would call this a prime number. Next, let's look at the number nine. The number nine has more than just two factors. Of course, the number one and nine itself are also factors. But another factor is three because three can divide into nine without having a remainder. Now, since the number nine has more than the two factors and it's not prime, we call it composite. Next, we have the number 29. There's only two factors for the number 29, one and 29. That makes it a prime number. And lastly we have the example 35. One, five, seven and 35 are all factors of 35. So we call it composite. So through factors are numbers that can divide into a number with no remainder left over. Prime numbers have only two factors, one and itself. Composite numbers are numbers that are not prime and have more than two factors. So now you can understand what factors are and how we can classify numbers based on how many factors they have.
