A number a is divisible by the number b if a \div b has actually a remainder of zero (0). For example, 15 divided by 3 is precisely 5 which indicates that the remainder is zero. Us then say the 15 is divisible through 3.

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In our various other lesson, we disputed the divisibility rules because that 7, 11, and also 12. This time, we will cover the divisibility rule or exam for2, 3, 4, 5, 6, 9, and 10. Think me, girlfriend will be able to learn them really quickly due to the fact that you may not understand that you currently have a simple and intuitive expertise of it. Because that instance, it is evident that all also numbers are divisible through 2. The is pretty much the divisibility rule for 2. The score of this divisibility rules lesson is to formalize what you already know.

Divisibility rules assist us to identify if a number is divisible by another without going through the actual division process such together the long department method. If the number in inquiry are numerically small enough, we may not need to use the rules to test because that divisibility. However, fornumbers whose values are large enough, we desire to have some rules to offer as “shortcuts” to assist us figure out if lock are without doubt divisible by every other.


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A number is divisible by2if the critical digit the the number is 0, 2, 4, 6, or 8.

Example 1: Is the number 246 divisible through 2?

Solution: because the critical digit that the number 246 end in 6, that way it is divisible by 2.

Example 2: which of the numbers 100, 514, 309, and 768 are divisible by 2?

Solution: If we research all four numbers, just the number 309 doesn’t finish with 0, 2, 4, 6, or 8. We can conclude that all the numbers above except 309 are divisible by 2.


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A number is divisible by 3 if the amount of the number 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. Because the amount of the number is divisible by the 3, thus the number 111 is likewise divisible by 3.

Example 2: Which one of the two numbers 522 and 713 is divisible through 3?

Solution: The sum of the number of 522 (5+2+2=9) is 9 i m sorry is divisible by 3. That renders 522 divisible through 3. However, the number 713 has actually 11 as the sum of its digits which is clearly not divisible by 3 therefore 713 is not divisible by 3. Therefore, just 522 is divisible through 3.


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A number is divisible by 4 if the last 2 digits of the number are divisible through 4.

Example 1: What is the only number in the set below is divisible by 4?

945, 736, 118, 429

Solution: Observe the last 2 digits the the four numbers in the set. An alert that 736 is the just number within the last two digits (36) is divisible by 4. We deserve to conclude the 736 is the just number in the set that is divisible by 4.

Example 2: True or False. The number 5,554 is divisible through 4.

Solution: The last 2 digits the the number 5,554 is 54 which is not divisible by 4. That way the offered number is no divisible through 4 for this reason the prize is false.


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A number is divisible by 5 if the critical digit the the number is 0 or 5.

Example 1: multiple Choice. I m sorry 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 critical digit of the number should be either 0 or 5. Going end the choices, just the number 20 is divisible through 5 so the prize is choice C.

Example 2: pick all the number that space divisible through 5.

A) 27

B) 105

C)556

D) 343

E) 600

Solution: Both 105 and 600 space divisible through 5 because they either finish in 0 or 5. Thus, alternatives B and E room the exactly answers.


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A number is divisible by 6 if the number is divisible by both 2 and also 3.

Example 1: Is the number 255 divisible through 6?

Solution: For the number 255 to it is in divisible by 6, it have to divisible by 2 and also 3. Let’s check first if the is divisible by 2. Keep in mind that 255 is not an also number (any number finishing in 0, 2, 4, 6, or 8) which makes it not divisible 2. There’s no require to examine further. We can now conclude that this is no divisible by 6. The price is NO.

Example 2: Is the number 4,608 divisible through 6?

Solution: A number is an even number so that is divisible by 2. Now inspect if the is divisible by 3. Let’s perform that by including all the number of 4,608 i beg your pardon is 4 + 6+ 0 + 8 = 18. Obviously, the amount of the digits is divisible by 3 due to the fact that 18 ÷ 3 = 6. Because the number 4,608 is both divisible through 2 and 3 then it must additionally be divisible through 6. The price is YES.


A number is divisible by 9 if the sum of the number is divisible by 9.

Example 1: Is the number 1,764 divisible by 9?

Solution: For a number to it is in divisible through 9, the amount of its digits must also be divisible by 9. Because that the number 1,764 we obtain 1 + 7 + 6 + 4 = 18. Because the sum of the number is 18 and is divisible by 9 thus 1,764 should be divisible through 9.

Example 2: pick all the numbers that space divisible by 9.

A) 7,065

B) 3,512

C) 8,874

D) 22,778

E) 48,069

Solution: Let’s add the digits of every number and also check if its sum is divisible by 9.

For 7,065, 7 + 0 + 6 + 5 = 18 i beg your pardon is divisible by 9.For 3,512, 3 + 5 + 1 + 2 = 11 i beg your pardon is NOT divisible through 9.For 8,874, 8 + 8 + 7 + 4 = 27 which is divisible through 9.For 22,778, 2 + 2 + 7 + 7 + 8 = 26 which is NOT divisible by 9.For 48,069, 4 + 8 + 0 + 6 + 9 = 27 i beg your pardon is divisible by 9.

Therefore, choices A, C, and also E space divisible by 9.


A number is divisible by 10 if the last digit that the number is 0.

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The numbers 20, 40, 50, 170, and also 990 space all divisible by 10 because their last digit is zero, 0. Top top the other hand, 21, 34, 127, and 468 space not divisible through 10 since they don’t finish with zero.

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Divisibility Rules because that 7, 11, and also 12


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