Video: Investigating Patterns in the Ones Digit of the Multiples of a Number

In this chart of numbers from 1 to 50, Matthew has colored all of the multiples of 4 starting at 4. What are the next 3 multiples? He notices that the ones digits follow a repeating pattern. Write the repeating part of this pattern.

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Video Transcript

In this chart of numbers from one to 50, Matthew has colored all of the multiples of four, starting at four. What are the next three multiples?

To find the next three multiples, let’s go ahead and add another line to this chart. After 50, we will include numbers 51 through 60. We need to determine which of these are multiples of four. If we look at the pattern, every fourth number is a multiple of four. Starting at 48, let’s count forward four spaces. One, two, three, four. 52 is the next multiple of four. We repeat this process and count by four after 52. One, two, three, four. 56 is a multiple of four. We found the next two multiples. But our question is asking for the next three multiples. So again, one, two, three, four. 60 is a multiple of four.

We answer the first part of our problem, what are the next three multiples, with 52, 56, 60.

But this problem has two parts. The second part says that Matthew notices the ones digits follow a repeating pattern. Write the repeating part of this pattern.

Let’s list out the multiples of four and try to see this pattern in the ones place. As we write down all the multiples, we want to make sure that the ones place lines up. Okay, let’s look specifically at the digits in the ones place. We can read out the digits in order. Four, eight, two, six, zero, four, eight, two, six, zero, four. We notice that these five digits — four, eight, two, six, zero — are repeating.

In multiples of four, the ones digits follow the pattern of four, eight, two, six, zero.

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