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

You are watching: What numbers are divisible by 2

In our other lesson, we questioned the divisibility rules because that 7, 11, and also 12. This time, we will cover the divisibility rule or test for**2**, **3**, **4**, **5**, **6**, **9**, and also **10**. Think me, you will have the ability to learn them really quickly due to the fact that you might not know that you currently have a basic and intuitive knowledge of it. For instance, the is noticeable that all also numbers are divisible through 2. That is pretty lot the divisibility ascendancy for **2**. The goal of this divisibility rule lesson is to define what you currently know.

Divisibility rules assist us to recognize if a number is divisible by one more without going with the actual division process such together the long department method. If the number in question are numerically little enough, we may not must use the rule to test because that divisibility. However, fornumbers whose worths are large enough, we want to have actually some rule to offer as “shortcuts” to help us number out if they are certainly 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 critical digit of the number 246 ends in 6, that means it is divisible by 2.

Example 2: i m sorry of the numbers 100, 514, 309, and 768 space divisible by 2?

Solution: If we study 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 through 2.

**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 through 3?

Solution:** **Let’s include the digits of the number 111. We have actually 1 + 1 + 1 = 3. Because the sum of the number is divisible by the 3, therefore the number 111 is likewise divisible through 3.

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

Solution: The amount of the digits of 522 (5+2+2=9) is 9 which is divisible by 3. That makes 522 divisible through 3. However, the number 713 has actually 11 together the amount of its digits which is plainly not divisible through 3 for this reason 713 is not divisible by 3. Therefore, only 522 is divisible by 3.

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

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

945, 736, 118, 429

Solution:** **Observe the last 2 digits the the four numbers in the set. Notification that 736 is the just number within the last 2 digits (36) is divisible through 4. We deserve to conclude that 736 is the only 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 of the number 5,554 is 54 which is no divisible by 4. That method the offered number is not divisible by 4 for this reason the price is **false**.

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

Example 1: lot of Choice. Which number is divisible by 5.

*A)* 68

*B)* 71

*C)* 20

*D)* 44

Solution: In order because that a number to be divisible through 5, the last digit that the number must be either 0 or 5. Going end the choices, just the number 20 is divisible by 5 for this reason the answer is choice** C**.

Example 2: pick all the numbers that room divisible by 5.

*A)* 27

B) 105

*C)*556

*D)* 343

E) 600

Solution: Both 105 and 600 room divisible by 5 due to the fact that they either finish in 0 or 5. Thus, choices **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 be divisible through 6, it should divisible by 2 and 3. Let’s check an initial if that is divisible through 2. Keep in mind that 255 is no an also number (any number ending in 0, 2, 4, 6, or 8) which renders it no divisible 2. There’s no need to inspect further. We can now conclude that this is no divisible through 6. The price is **NO**.

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

Solution: A number is an even number so the is divisible by 2. Now check if that is divisible by 3. Let’s perform that by adding all the digits of 4,608 which is 4 + 6+ 0 + 8 = 18. Obviously, the amount of the number is divisible by 3 since 18 ÷ 3 = 6. Due to the fact that the number 4,608 is both divisible by 2 and also 3 climate it must also be divisible by 6. The answer is **YES**.

**A number is divisible by 9 if the amount of the digits 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 sum of its number must likewise be divisible by 9. For the number 1,764 we acquire 1 + 7 + 6 + 4 = 18. Since the amount of the digits is 18 and is divisible by 9 therefore 1,764 have to be divisible by 9.

Example 2: pick all the number that room divisible through 9.

*A)* 7,065

*B)* 3,512

*C)* 8,874

*D)* 22,778

*E)* 48,069

Solution:** **Let’s add the number of each number and also check if its amount is divisible by 9.

**NOT**divisible through 9.For 8,874, 8 + 8 + 7 + 4 = 27 i beg your pardon is divisible through 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 through 9.

Therefore, selections **A**, **C**, and **E** are divisible by 9.

**A number is divisible by 10 if the last digit the the number is 0.See more: Do Gold And Pink Go Together, 10 Best Colors That Go With Gold (With Pictures)**

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

**You might also be interested in:**

Divisibility Rules because that 7, 11, and 12

**MATH SUBJECTS**Introductory AlgebraIntermediate AlgebraAdvanced AlgebraAlgebra indigenous ProblemsGeometryIntro come Number TheoryBasic math Proofs

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