# Divisibility rules

Students will be able to use divisibility rules to determine factors of whole numbers. Introduction 5 minutes Write a large number on the board e. By the end of our lesson, you will know some shortcuts that will make it easy for you to determine if numbers, even huge numbers like this, are divisible by other numbers like 2, 3, ! Any integer is divisible by 1.

## Divisibility rule - Wikipedia

The last digit is even 0, 2, 4, 6, or 8. The result must be divisible by 3. Subtract the quantity of the digits 2, 5, and 8 in the number from the quantity of the digits 1, 4, and 7 in the number. Using the example above: The last two digits form a number that is divisible Divisibility rules 4.

If the tens digit is even, the ones digit must be 0, 4, or 8. If the tens digit is odd, the ones digit must be 2 or 6. Twice the tens digit, plus the ones digit is divisible by 4.

The last digit is 0 or 5. Forming an alternating sum of blocks of three from right to left gives Divisibility rules multiple of 7   1, Works because 21 is divisible by 7. Adding 5 times the last digit to the rest gives a multiple of 7. Works because 49 is divisible by 7. Adding the last two digits to twice the rest gives a multiple of 7. Works because 98 is divisible by 7. Multiply each digit from right to left by the digit in the corresponding position in this pattern from left to right: Adding the results gives a multiple of 7.

Adding the last digit to 3 times the rest gives a multiple of 7. If the hundreds digit is odd, the number obtained by the last two digits plus 4 must be divisible by 8. Add the last digit to twice the rest. The result must be divisible by 8. The last three digits are divisible by 8.

Examine divisibility of just The result must be divisible by 9. The ones digit is 0. Form the alternating sum of the digits. The result must be divisible by Add the digits in blocks of two from right to left. Subtract the last digit from the rest. Add the last digit to the hundreds place add 10 times the last digit to the rest.

If the number of digits is even, add the first and subtract the last digit from the rest. Subtract the last digit from twice the rest. Form the alternating sum of blocks of three from right to left.

Subtract the last two digits from four times the rest. Subtract 9 times the last digit from the rest. It is divisible by 2 and by 7.

Add the last two digits to twice the rest. It is divisible by 3 and by 5.2: Any number that ends in an even digit (0, 2, 4, 6, 8) is divisible by 2. 5: If the last digit is zero or 5, then the number is divisible by 5. Any number ending in zero is divisible by 3: If the digit sum is divisible by 3, then the number is divisible by 3.

6: Any even number that is divisible by 3 is also divisible by 6. 9: If the digit sum is divisible by 9, then the number is. Divisibility rules worksheet for 2,3,4,5 and 6 Divisibility rules worksheet for 2,4,8,5 and 10 Divisibility rules worksheet for 3,6 and 9 Is it Divisible by 10?