# Divisibility by 5, 6, and 7

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• 0:01 Divisibility
• 0:58 By 5
• 2:04 By 6
• 3:11 By 7
• 3:58 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, we will see what numbers can be divided equally by 5, 6, and 7. Learn the pattern that you can use to find other numbers divisible by 5, 6 and 7. Learn how you can visualize divisibility.

## Divisibility

Do you remember what it means for something to have divisibility? It means that it can be divided equally by a certain number. So, if a number has divisibility by 5, then it means it can be divided equally by 5. If we think of splitting a bunch of candies evenly into bowls, then divisibility by 5 means that we can split the number of candies evenly between 5 bowls. We also use the word 'divisible.' If we can divide 10 candies equally between 5 bowls, we also say that 10 is divisible by 5.

Do you remember the division symbol? Yes, it's the symbol that looks like a horizontal line with a dot on top and a dot on bottom. When we divide, we find the number of candies that each bowl will have. So, 10 divided by 5 is 2, since each bowl will end up with 2 candies. In this video lesson, we look at numbers that are divisible by 5, 6, and 7. Let's begin.

## By 5

If something is divisible by 5, then that means we can split it evenly between 5 bowls. We will stick to our candies and bowls example throughout this video lesson. Look, here are your 5 bowls. Can you think of the very first number that is divisible by 5? Yes, it is 5. If we put 1 candy in each bowl, we will have 5 candies total. So, 5 is divisible by 5. 5 divided by 5 is 1.

What's the next number? If we add one more candy to each bowl, we will have 10 candies total. So, 10 is also divisible by 5. 10 divided by 5 is 2. Do you see what's going on here? If we keep adding 5 to our previous number, we will find our next number that is divisible by 5. What is our next number? 15. And after that? 20. Look at the numbers and you might see a pattern. All the numbers that are divisible by 5 end in either 0 or 5. This is another quick way to determine whether a number is divisible by 5.

## By 6

Now, what about divisibility by 6? Yes, this also has the same pattern as divisibility by 5, except we now keep adding 6 to our previous number. Here are your 6 bowls now. What is the first number that is divisible by 6? Add 1 candy to each bowl. How many candies do you get? 6. 6 divided by 6 is 1. The next number? 12. 12 divided by 6 is 2. Can you figure out the next number? Did you get 18? If so, great! You got it!

There is no pattern to these numbers like there is for the number 5. But there is a rule you can follow. This rule is that the number has to be even, and if you add up the individual digits of the number, they will add up to a number that is divisible by 3. For example, the number 18 is even, and when you add up the individual digits of the numbers (1 + 8 = 9), you get a number that is divisible by 3 (9 / 3 = 3).

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