What is the divisibility rule of 2 3 4 5 6 7 8 9 10?

The divisibility rules for numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10 provide quick ways to determine if one integer can be divided by another without a remainder. These rules are based on the properties of the numbers themselves and can significantly speed up mathematical calculations. Understanding these shortcuts is essential for students and anyone working with numbers.

Unlocking the Mysteries of Divisibility Rules

Divisibility rules are mathematical shortcuts. They help us quickly see if a number can be divided evenly by another. Instead of performing long division, we can use simple checks. This knowledge is incredibly useful in everyday math and problem-solving.

The Divisibility Rule of 2

A number is divisible by 2 if its last digit is even. This means the number ends in 0, 2, 4, 6, or 8.

For example, 124 is divisible by 2 because it ends in 4. The number 357 is not divisible by 2 because it ends in 7, which is an odd digit.

The Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is divisible by 3. You add up all the digits in the number. If that sum can be divided by 3 without a remainder, the original number can too.

Consider the number 234. The sum of its digits is 2 + 3 + 4 = 9. Since 9 is divisible by 3 (9 ÷ 3 = 3), 234 is also divisible by 3.

The Divisibility Rule of 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. You only need to look at the tens and units place.

Let’s take 1,316. The last two digits form the number 16. Since 16 is divisible by 4 (16 ÷ 4 = 4), 1,316 is divisible by 4.

The Divisibility Rule of 5

A number is divisible by 5 if its last digit is either 0 or 5. This is one of the easiest rules to remember.

Examples include 75, which ends in 5, and 230, which ends in 0. Both are divisible by 5.

The Divisibility Rule of 6

A number is divisible by 6 if it is divisible by both 2 and 3. This rule combines the first two we discussed. If a number meets both criteria, it will be divisible by 6.

Take the number 468. It’s divisible by 2 because it ends in 8. The sum of its digits is 4 + 6 + 8 = 18. Since 18 is divisible by 3 (18 ÷ 3 = 6), 468 is also divisible by 3. Because it’s divisible by both 2 and 3, 468 is divisible by 6.

The Divisibility Rule of 7

The divisibility rule for 7 is a bit more complex. You double the last digit of the number and subtract it from the remaining digits. If the result is divisible by 7 (or is 0), then the original number is divisible by 7. You may need to repeat this process.

Let’s test 343. Double the last digit (3) to get 6. Subtract this from the remaining digits (34): 34 – 6 = 28. Since 28 is divisible by 7 (28 ÷ 7 = 4), 343 is divisible by 7.

The Divisibility Rule of 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. This rule is similar to the rule for 4 but extends to the hundreds place.

Consider the number 5,120. The last three digits form 120. If we divide 120 by 8, we get 15. Therefore, 5,120 is divisible by 8.

The Divisibility Rule of 9

A number is divisible by 9 if the sum of its digits is divisible by 9. This is very similar to the rule for 3, but the sum must be a multiple of 9.

Take the number 729. The sum of its digits is 7 + 2 + 9 = 18. Since 18 is divisible by 9 (18 ÷ 9 = 2), 729 is divisible by 9.

The Divisibility Rule of 10

A number is divisible by 10 if its last digit is 0. This is the simplest rule of all.

Any number ending in a zero, such as 150, 2,000, or 990, is divisible by 10.

Quick Reference Table for Divisibility Rules

Here’s a handy table summarizing these essential divisibility rules:

Why Are Divisibility Rules Important?

Mastering these divisibility rules can transform how you approach math problems