A number is divisible by 2 if the last digit of the number is 0, 2, 4, 6, or 8.
Example 1: Is the number 246 divisible by 2?
Solution: Since the last digit of the number 246 ends in 6, that means it is divisible by 2.
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
Example 1: Is the number 111 divisible by 3?
Solution: Let’s add the digits of the number 111. We have 1 + 1 + 1 = 3. Since the sum of the digits is divisible by the 3, therefore the number 111 is also divisible by 3.
A number is divisible by 4 if the last two digits of the number are divisible by 4.
Example 1: What is the only number in the set below is divisible by 4?
{945, 736, 118, 429}
Solution: Observe the last two digits of the four numbers in the set. Notice that 736 is the only number wherein the last two digits (36) is divisible by 4. We can conclude that 736 is the only number in the set that is divisible by 4.
A number is divisible by 5 if the last digit of the number is 0 or 5.
Example 1: Multiple Choice. Which number is divisible by 5.
A) 68
B) 71
C) 20
D) 44
Solution: In order for a number to be divisible by 5, the last digit of the number must be either 0 or 5. Going over the choices, only the number 20 is divisible by 5 so the answer is choice C.
A number is divisible by 6 if the number is divisible by both 2 and 3.
Example 2: Is the number 4,608 divisible by 6?
Solution: A number is an even number so it is divisible by 2. Now check if it is divisible by 3. Let’s do that by adding all the digits of 4,608 which is 4 + 6+ 0 + 8 = 18. Obviously, the sum of the digits is divisible by 3 because 18 ÷ 3 = 6. Since the number 4,608 is both divisible by 2 and 3 then it must also be divisible by 6. The answer is YES.
A number is divisible by 9 if the sum of the digits is divisible by 9.
Example 1: Is the number 1,764 divisible by 9?
Solution: For a number to be divisible by 9, the sum of its digits must also be divisible by 9. For the number 1,764 we get 1 + 7 + 6 + 4 = 18. Since the sum of the digits is 18 and is divisible by 9 therefore 1,764 must be divisible by 9.
A number is divisible by 10 if the last digit of the number is 0.
The numbers 20, 40, 50, 170, and 990 are all divisible by 10 because their last digit is zero. On the other hand, 21, 34, 127, and 468 are not divisible by 10 since they don’t end with zero.
Answers & Comments
Answer:
Any term is divisible by 2 if its last digit is (0,2,4,6,8)
Step-by-step explanation:
A number is divisible by 2 if the last digit of the number is 0, 2, 4, 6, or 8.
Example 1: Is the number 246 divisible by 2?
Solution: Since the last digit of the number 246 ends in 6, that means it is divisible by 2.
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
Example 1: Is the number 111 divisible by 3?
Solution: Let’s add the digits of the number 111. We have 1 + 1 + 1 = 3. Since the sum of the digits is divisible by the 3, therefore the number 111 is also divisible by 3.
A number is divisible by 4 if the last two digits of the number are divisible by 4.
Example 1: What is the only number in the set below is divisible by 4?
{945, 736, 118, 429}
Solution: Observe the last two digits of the four numbers in the set. Notice that 736 is the only number wherein the last two digits (36) is divisible by 4. We can conclude that 736 is the only number in the set that is divisible by 4.
A number is divisible by 5 if the last digit of the number is 0 or 5.
Example 1: Multiple Choice. Which number is divisible by 5.
A) 68
B) 71
C) 20
D) 44
Solution: In order for a number to be divisible by 5, the last digit of the number must be either 0 or 5. Going over the choices, only the number 20 is divisible by 5 so the answer is choice C.
A number is divisible by 6 if the number is divisible by both 2 and 3.
Example 2: Is the number 4,608 divisible by 6?
Solution: A number is an even number so it is divisible by 2. Now check if it is divisible by 3. Let’s do that by adding all the digits of 4,608 which is 4 + 6+ 0 + 8 = 18. Obviously, the sum of the digits is divisible by 3 because 18 ÷ 3 = 6. Since the number 4,608 is both divisible by 2 and 3 then it must also be divisible by 6. The answer is YES.
A number is divisible by 9 if the sum of the digits is divisible by 9.
Example 1: Is the number 1,764 divisible by 9?
Solution: For a number to be divisible by 9, the sum of its digits must also be divisible by 9. For the number 1,764 we get 1 + 7 + 6 + 4 = 18. Since the sum of the digits is 18 and is divisible by 9 therefore 1,764 must be divisible by 9.
A number is divisible by 10 if the last digit of the number is 0.
The numbers 20, 40, 50, 170, and 990 are all divisible by 10 because their last digit is zero. On the other hand, 21, 34, 127, and 468 are not divisible by 10 since they don’t end with zero.