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

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In our various other lesson, we questioned the divisibility rules because that 7, 11, and 12. This time, we will certainly cover the divisibility rule or tests for2, 3, 4, 5, 6, 9, and 10. Believe me, girlfriend will be able to learn them very quickly because you may not recognize that you currently have a straightforward and intuitive understanding of it. For instance, it is obvious that all also numbers space divisible through 2. The is pretty lot the divisibility dominion for 2. The goal of this divisibility rules lesson is to formalize what you currently know.

Divisibility rules help us to determine if a number is divisible by another without going v the actual department process such as the long department method. If the number in inquiry are numerically small enough, we might not have to use the rule to test because that divisibility. However, fornumbers whose values are large enough, we want to have actually some rule to serve as “shortcuts” to assist us figure out if lock are undoubtedly divisible by each other. A number is divisible by2if the last digit of the number is 0, 2, 4, 6, or 8.

Example 1: Is the number 246 divisible by 2?

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

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

Solution: If we research all four numbers, only the number 309 doesn’t end with 0, 2, 4, 6, or 8. We deserve to conclude the all the numbers above except 309 space divisible through 2. A number is divisible by 3 if the amount of the digits of the number is divisible through 3.

Example 1: Is the number 111 divisible by 3?

Solution: Let’s include the number of the number 111. We have 1 + 1 + 1 = 3. Since the amount of the number is divisible by the 3, as such the number 111 is likewise divisible by 3.

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

Solution: The amount of the digits of 522 (5+2+2=9) is 9 which is divisible through 3. That provides 522 divisible by 3. However, the number 713 has 11 as the sum of its digits which is plainly not divisible through 3 therefore 713 is not divisible by 3. Therefore, only 522 is divisible by 3. A number is divisible by 4 if the last two digits the the number are divisible by 4.

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

945, 736, 118, 429

Solution: Observe the last 2 digits the the 4 numbers in the set. Notice that 736 is the only number within the last 2 digits (36) is divisible by 4. We deserve to conclude the 736 is the only number in the set that is divisible by 4.

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

Solution: The last two digits of the number 5,554 is 54 i beg your pardon is not divisible through 4. That method the provided number is no divisible by 4 therefore the price is false. A number is divisible by 5 if the critical digit that the number is 0 or 5.

Example 1: multiple Choice. I beg your pardon number is divisible through 5.

A) 68

B) 71

C) 20

D) 44

Solution: In order for a number to it is in divisible by 5, the critical digit that the number need to be either 0 or 5. Going over the choices, only the number 20 is divisible through 5 for this reason the price 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 also 600 are divisible by 5 since they either end in 0 or 5. Thus, options B and also E are the correct answers. A number is divisible by 6 if the number is divisible by both 2 and 3.

Example 1: Is the number 255 divisible by 6?

Solution: For the number 255 to it is in divisible by 6, it need to divisible by 2 and also 3. Let’s check very first if the is divisible through 2. Note that 255 is not an even number (any number finishing in 0, 2, 4, 6, or 8) which makes it no divisible 2. There’s no need to inspect further. We deserve to now conclude the this is not divisible by 6. The answer is NO.

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

Solution: A number is an even number so the is divisible by 2. Now inspect if the is divisible through 3. Let’s do that by adding all the digits of 4,608 i m sorry is 4 + 6+ 0 + 8 = 18. Obviously, the sum of the digits is divisible by 3 since 18 ÷ 3 = 6. Because the number 4,608 is both divisible by 2 and also 3 climate it must likewise be divisible by 6. The prize is YES.

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

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

Solution: For a number to be divisible through 9, the amount of its number must additionally be divisible by 9. Because that the number 1,764 we obtain 1 + 7 + 6 + 4 = 18. Due to the fact that the amount of the number is 18 and also is divisible by 9 because of this 1,764 should be divisible through 9.

Example 2: choose all the number that space divisible by 9.

A) 7,065

B) 3,512

C) 8,874

D) 22,778

E) 48,069

Solution: Let’s include the digits of each number and check if its amount 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 which is NOT divisible through 9.For 8,874, 8 + 8 + 7 + 4 = 27 i beg your pardon is divisible by 9.For 22,778, 2 + 2 + 7 + 7 + 8 = 26 i m sorry is NOT divisible by 9.For 48,069, 4 + 8 + 0 + 6 + 9 = 27 which is divisible by 9.

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

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

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The number 20, 40, 50, 170, and also 990 room all divisible by 10 because their last digit is zero, 0. Top top the other hand, 21, 34, 127, and also 468 are not divisible through 10 due to the fact that they don’t end with zero.

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