Learn the facts and tricks of divisibility rules: 3rd Grade worksheets

The divisibility rule for 2, 5, and 10 is easy and useful. It helps you quickly check if a number can be divided by 2, 5, or 10 without doing any calculations. Here's how it works:

• A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
• A number is divisible by 5 if its last digit is 0 or 5.
• A number is divisible by 10 if its last digit is 0.

For example, let's look at the number 450. Its last digit is 0, so it is divisible by 2, 5, and 10. You can easily confirm this by dividing it by each of these numbers and getting a whole number as the answer:

• 450 ÷ 2 = 225
• 450 ÷ 5 = 90
• 450 ÷ 10 = 45

Now let's look at another number: 357. Its last digit is 7, which is odd, not 0 or 5. So it is not divisible by 2, 5, or 10. You can also verify this by trying to divide it by each of these numbers and getting a decimal or a remainder as the answer:

• 357 ÷ 2 = 178.5
• 357 ÷ 5 = 71.4
• 357 ÷ 10 = 35.7

You can use this rule to quickly test any number for divisibility by 2, 5, or 10. It's a great way to save time and mental energy when doing division problems.

The divisibility rule for 3 and 9 is more tricky than the one for 2, 5, and 10, but it's still handy and fun. It helps you check if a number can be divided by 3 or 9 by looking at the sum of its digits. Here's how it works:

• A number is divisible by 3 if the sum of its digits is divisible by 3.
• A number is divisible by 9 if the sum of its digits is divisible by 9.

  For example, let's look at the number 729. To find the sum of its digits, we add them up:

  `7 + `2 + `9 = `18

  The sum of the digits is `18`, divisible by `3` and `9`. So we can conclude that `729` is also divisible by `3` and `9`. We can check this by dividing it by each of these numbers and getting a whole number as the answer:

  `729` ÷ `3` = `243`

  `729` ÷ `9` = `81`

• Now let's look at another number: `532`. To find the sum of its digits, we add them up:

  `5 + `3 + `2 = `10

  The sum of the digits is `10`, which is not divisible by either `3` or `9`. So we can conclude that `532` is not divisible by `3` or `9`.

You can use this rule to quickly test any number for divisibility by `3` or `9`. It's a good way to practice your addition and mental math skills.

The divisibility rule for `4` and `8` is similar to the one for `2`, but it involves looking at the last two digits instead of just the last one. It helps you check if a number can be divided by `4` or `8` by looking at whether the last two digits form a number divisible by `4` or `8`. Here's how it works:

• A number is divisible by `4` if its last two digits are divisible by `4`.
• A number is divisible by `8` if its last three digits are divisible by `8`.

For example, let's look at the number `1236`. To check if it is divisible by `4`, we look at its last two digits: `36`. `36` is divisible by `4`, so we can conclude that `1236` is also divisible by `4`. We can confirm this by dividing it by `4` and getting a whole number as the answer:

`1236` ÷ `4` = `309`

To check if it is divisible by `8`, we look at its last three digits: `236`. `236` is not divisible by `8`, so we can conclude that `1236` is not divisible by `8`. We can also verify this by trying to divide it by `8` and getting a decimal or a remainder as the answer:

`1236` ÷ `8` = `154.5`

Now let's look at another number: `4096`. To check if it is divisible by `4`, we look at its last two digits: `96`. `96` is divisible by `4`, so we can conclude that `4096` is also divisible by `4`. We can check this by dividing it by `4` and getting a whole number as the answer:

`4096` ÷ `4` = `1024`

To check if it is divisible by `8`, we look at its last three digits: `096`. `096` is divisible by `8`, so we can conclude that `4096` is also divisible by `8`. We can check this by dividing it by `8` and getting a whole number as the answer:

`4096` ÷ `8` = `512`

You can use this rule to test any number for divisibility by 4 or 8. It's a useful way to improve your division skills and number sense.

You will notice that the divisibility rules for 6 and 12 are related to the rules for 2 and 3. That's because 6 is the product of 2 and 3, and 12 is the product of 2 and 2 and 3. So, to check if a number is divisible by 6, check if it is divisible by 2 and 3. And to check if a number is divisible by 12, you need to check if it is divisible by both 4 and 3. Here are some examples:

• Is 48 divisible by 6? Yes, because it is divisible by both 2 (it ends in an even digit) and 3 (the sum of its digits is 12, which is divisible by 3).
• Is 72 divisible by 12? Yes, because it is divisible by both 4 (the last two digits form a number divisible by 4) and 3 (the sum of its digits is 9, which is divisible by 3).
• Is 63 divisible by 6? No, because it is not divisible by 2 (it ends in an odd digit).
• Is 64 divisible by 12? No, because it is not divisible by 4 (the last two digits form a number not divisible by 4).

Now that you have learned the basic divisibility rules for the most common factors, you might be wondering how to remember them all. Don't worry. Our Mathskills4kids 3rd Grade worksheets have designed fun tips to learn the facts and tricks of divisibility rules and remember them always.

They include:

• For the divisibility rule for 2, you can think of a rhyme: If it ends in zero or an even number, then it's divisible by two - no wonder!
• For the divisibility rule for 3, you can think of a song: Add up all the digits and see if they're divisible by three - yippee!
• For the divisibility rule for 4, you can think of a word: Look at the last two digits - that's the key if they're divisible by four - easy peasy!
• For the divisibility rule for 5, you can think of a gesture: Hold up your hand and count your fingers - one, two, three, four, five. If it ends in zero or five - high five!
• For the divisibility rule for 6, you can think of a rule: If it's divisible by two and three - then it's also divisible by six - easy breezy!
• For the divisibility rule for 8, you can think of a trick: Cut off the last three digits and see if they're divisible by eight - great!
• For the divisibility rule for 9, you can think of a game: Add up all the digits and see if they're divisible by nine - fine!
• For the divisibility rule for 10, you can think of a fact: If it ends in zero - then it's divisible by ten - super!

You might be wondering why you need to learn divisibility rules. After all, you can always use a calculator or long division to find out if a number is divisible by another number. Well, divisibility rules are not only useful for math class. They can also help you in everyday situations where you will divide or simplify numbers quickly.

Here are some real-world examples of using divisibility rules:

• Suppose you want to split a pizza among your friends. You can use the divisibility rule for 2 to check if the number of slices is even or odd. If it's even, you can divide it equally among your friends. If it's odd, you can cut one slice in half or leave one for yourself.
• Suppose you want to buy some candy bars at the store. You can use the divisibility rule for 3 to check if the price of each candy bar is a multiple of three. If it is, pay with a dollar bill and get no change. If not, buy more candy bars or pay with coins.
• Suppose you want to arrange some books on a shelf. You can use the divisibility rule for 4 to check if the number of books is a multiple of four. If it is, you can arrange them in rows of four. If it's not, you can leave some space on the shelf or stack some books on each other.
• Suppose you want to tip a waiter at a restaurant. You can use the divisibility rule for 5 to check if the bill amount is a multiple of five. If it is, you can tip 20% by moving the decimal point one place to the left and doubling the result. If not, you can either round up or down the bill amount to the nearest multiple of five and then tip 20%.