Divisibility and Divisibility Rules

🌟 Definition of Divisibility:

When you divide a number and there’s no remainder, the number is divisible by the other.

🍌 Example 1:

$ 9 \div 2 = 4 \text{ R }1$

The remainder is 1, so 9 is not divisible by 2.

🍌 Example 2:

$ 9 \div 3 = 3$

There’s no remainder, so 9 is divisible by 3.

Divisibility rules help you quickly check if a number is divisible without doing the full division.

💡 Divisible by 2:

Rule: Look at the last digit. If it’s 0, 2, 4, 6, or 8, the number is divisible by 2.

Example: Is 26 divisible by 2?

• 26 ends in 6, which is even.
• So, 26 is divisible by 2.

💡 Divisible by 4:

Rule: Look at the last two digits. If those digits make a number divisible by 4, the whole number is divisible by 4.

Example: Is 328 divisible by 4?

• The last two digits of 328 are 28. 
• 28 is divisible by 4, so 328 is divisible by 4.

💡Divisible by 8:

Rule: Look at the last three digits. If that number is divisible by 8, then the whole number is.

Example:

• The last three digits of 6160 are 160.
• 160 is divisible by 8, so 6160 is divisible by 8.

💡Divisible by 3:

Rule: Add all the digits. If the sum is divisible by 3, then the whole number is divisible by 3.

Example: Is 543 divisible by 3?

• Adding all digits: 5 + 4 + 3 = 12
• 12 is divisible by 3, so 543 is divisible by 3.

💡 Divisible by 9:

Rule: Add all the digits. If the sum is divisible by 9, then the number is divisible by 9.

Example: Is 198 divisible by 9?

• Adding all digits: 1 + 9 + 8 = 18
• 18 is divisible by 9, so 198 is divisible by 9.

💡Divisible by 6:

Rule: Check if the number is divisible by both 2 and 3. If it passes both checks, then the number is divisible by 6.

Example: Is 402 divisible by 6?

• The last digit is 2, so 402 is divisible by 2.
• The sum of all digits is 4 + 0 + 2 = 6.
• 6 is divisible by 3, so 402 is divisible by 3.
• Since 402 is divisible by 2 and 3, 402 is divisible by 6.

💡Divisible by 5:

Rule: A number is divisible by 5 if its last digit is 0 or 5.

Example: Is 415 divisible by 5?

• The last digit is 5, so 415 is divisible by 5.

💡Divisible by 10:

Rule: A number is divisible by 10 if its last digit is 0.

Example: Is 320 divisible by 10?

• The last digit is 0, so 320 is divisible by 10.