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

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In our other lesson, we questioned the divisibility rules because that 7, 11, and also 12. This time, we will certainly cover the divisibility rule or exam for2, 3, 4, 5, 6, 9, and 10. Think me, girlfriend will be able to learn them very quickly due to the fact that you may not understand that you already have a simple and intuitive understanding of it. Because that instance, that is noticeable that all even numbers are divisible by 2. That is pretty lot the divisibility ascendancy for 2. The score of this divisibility rule lesson is to formalize what you already know.

Divisibility rules aid us to identify if a number is divisible by another without going v the actual department process such together the long division method. If the number in concern are numerically small enough, we might not must use the rules to test for divisibility. However, fornumbers whose worths are huge enough, we desire to have some rules to serve as “shortcuts” to aid us figure out if they are undoubtedly divisible by each other. A number is divisible by2if the last digit that the number is 0, 2, 4, 6, or 8.

Example 1: Is the number 246 divisible by 2?

Solution: since the last digit the the number 246 ends in 6, that means it is divisible through 2.

Example 2: i beg your pardon of the number 100, 514, 309, and also 768 room divisible by 2?

Solution: If we study all 4 numbers, only the number 309 doesn’t end with 0, 2, 4, 6, or 8. We can conclude that all the numbers over except 309 are divisible by 2. A number is divisible by 3 if the sum of the number of the number is divisible by 3.

Example 1: Is the number 111 divisible by 3?

Solution: Let’s add the number of the number 111. We have 1 + 1 + 1 = 3. Because the sum of the digits is divisible by the 3, as such the number 111 is likewise divisible through 3.

Example 2: Which among the 2 numbers 522 and also 713 is divisible by 3?

Solution: The sum of the digits of 522 (5+2+2=9) is 9 which is divisible by 3. That renders 522 divisible through 3. However, the number 713 has actually 11 together the sum of its digits which is plainly not divisible by 3 thus 713 is not divisible by 3. Therefore, only 522 is divisible through 3. 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 that the four numbers in the set. An alert that 736 is the just number inside the last 2 digits (36) is divisible through 4. We can conclude that 736 is the just 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 2 digits the the number 5,554 is 54 i m sorry is no divisible by 4. That way the provided number is no divisible through 4 therefore the price is false. A number is divisible by 5 if the last digit the the number is 0 or 5.

Example 1: lot of Choice. I m sorry number is divisible through 5.

A) 68

B) 71

C) 20

D) 44

Solution: In order because that a number to be divisible through 5, the last digit the the number have to be either 0 or 5. Going over the choices, only the number 20 is divisible by 5 so the price is choice C.

Example 2: choose all the numbers that space divisible by 5.

A) 27

B) 105

C)556

D) 343

E) 600

Solution: Both 105 and also 600 are divisible by 5 because they either end in 0 or 5. Thus, alternatives B and E room the exactly 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 through 6, it should divisible by 2 and 3. Let’s check an initial if it is divisible through 2. Note that 255 is no an also number (any number ending in 0, 2, 4, 6, or 8) which makes it not divisible 2. There’s no require to check 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 by 6?

Solution: A number is an even number so that is divisible by 2. Now check if the is divisible through 3. Let’s do that by adding all the number of 4,608 i m sorry is 4 + 6+ 0 + 8 = 18. Obviously, the amount of the number is divisible through 3 due to the fact that 18 ÷ 3 = 6. Since the number 4,608 is both divisible through 2 and 3 climate it must additionally be divisible by 6. The price 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 number must additionally be divisible by 9. For the number 1,764 we get 1 + 7 + 6 + 4 = 18. Because the amount of the digits is 18 and also is divisible through 9 as such 1,764 must 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 each number and check if its sum is divisible through 9.

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

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

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

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

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