How Can You Tell if a Number Is Divisible by 4
There are many shortcuts or tricks that permit you to test whether a number, or dividend, is divisible by a given divisor. This page focuses on the nearly-frequently studied divisibility rules which involve divisibility by 2, iii, 4, 5, 6, 8, 9, 10, and past 11
- Rules:
- divisible by ii
- by 3
- by 4
- by 5
- past half-dozen
- by eight
- by ix
- by 10
- by eleven
What is the divisibility by 2 Dominion?
Answer:Almost everyone is familiar with this rule, which states that any fifty-fifty number tin can be divided past 2.
Even numbers are multiples of two. A number is fifty-fifty if information technology ends in 0, ii, four, vi, or eight.
Examples of numbers that are even and therefore laissez passer this divisibility test.
| Number | Explanation |
| ane2 | Since the concluding digit is a 2, the entire number, 12, is an even numberand therefore divisible by 2. |
| 318 | Since the last digit is an 8, this is an an even number and therefore divisible by 2. |
| -310 | Since the concluding digit is 0, this is an an even number and therefore divisible past 2. |
| -32,814 | Since the last digit is a 4, this is an fifty-fifty number and therefore divisible by 2. |
Check if any number is divisible by two. Type in any number that you want, and the calculator will apply the rule for divisibility by 2 to explain the upshot.
See what the rule for divisibility by two has to say about the following number:
Examples of numbers that are do not pass this divisibility test because they are non fifty-fifty.
| Number | Explanation |
| iii | 3 is non an even number. |
| 103 | Not an even number. |
| 157 | Not an even number. |
| 221 | Not an even number. |
- Rules:
- divisible by 2
- past three
- by 4
- past five
- by 6
- past 8
- past ix
- by x
- by 11
What is the divisibility by 3 dominion?
Reply:Rule: A number is divisible by 3 if the sum of its digits is divisible past iii.
375, for instance, is divisible by 3 since sum of its digits (3+7+v) is 15. And 15 is divisible by 3.
| Number | Explanation |
| 12 | $$ 1 + 2 = 3$$ and three is divisible past 3. |
| 36 | $$ iii + 6 = 9 $$ and 9 is divisible by three. |
| 102 | $$1 + 0 + 2 = 3$$ and 3 is divisible by 3. |
| 100,002,000 | $$ 100,002,000 = 1 + 0 + 0 + 0 + 0 + 2 + 0 + 0 + 0 = three$$ and 3 is divisible by 3. |
| 36 | $$ 3 + 6 = 9 $$ and 9 is divisible by 3. |
Check if the following number: is evenly divisible past iii.
| Number | Caption |
| xiv | 1 + 4 = 5 and since 5 is not divisible by 3, so xiv is also not. |
| 124 | $$1 + two + iv = seven$$ which is no good, since seven is non evenly divisible by 3. |
| 100,002,001 | $$1 + 0 + 0 + 0 + ii + 0 + 0 + 1 = 4$$ so this very large also does non pass this divisibility test. |
- Rules:
- divisible past 2
- by iii
- by 4
- by v
- by half-dozen
- by 8
- past 9
- by 10
- by xi
What is the divisibility by iv rule?
Answer:Rule: A number is divisible past four if the number's terminal two digits are divisible by 4.
9,312, for instance, is divisible by 4 since its final 2 digits are 12. And 12 is divisible by iv.
Examples of numbers that are divisible by iv:
| Number | Caption |
| one12 | Since the last two digits, 12, are divisible past 4, the number 112 is also divisible by 4. |
| 10,948 | The last two digits, 48, are divisible by 4. Therefore, the whole number is also. |
| 100,002,088 | Yep, this satisfies dominion because 88 is divisible by four! |
| -12,036 | 36 and 36 is evenly divided by 4, so -12,036 passes the test! |
See if the following is evenly divisible by four.
Examples of numbers that are practise not laissez passer this divisibility test.
| Number | Explanation |
| 113 | Since the last two digits, 13, are not divisible by 4, the whole number does non pass this divisibility exam. |
| x,941 | The terminal 2 digits, 41, are not de visible by 4. Therefore, the whole number does not satisfy the rule for 4. |
| 100,002,0xiv | Those final two digits, 14, practice not work. |
| -1,011 | 11 is non divisible past 4, and so one,011 fails this test. |
Ever wonder why these rules work. The examination for 4 makes sense if you just intermission down the numbers. Retrieve about what this dominion says: "All that matters is whether or not the last two digits are divisible by iv." Allow's await at why this rule is truthful.
Examine some iii digit numbers- 124 is the aforementioned as 100 + 24, and we know that 100 is divisible by four so all that matters here is whether or not 24, or the concluding two digits, are divisible by 4. The same could be said for any three digit number 224 = 200 + 24, and nosotros know that 200 is divisible past iv so again all that we're worried almost are these terminal ii digits.
- Any multiple of 100 is divisible by four! Whether yous're talking about 300, 700, one thousand, 1100, 123,000 -- All of these multiples of 100 are divisible by 4, which means that all that we e'er have to worry nigh is the last 2 digits!
- Rules:
- divisible by two
- past 3
- by four
- by 5
- by 6
- by 8
- past 9
- past ten
- past 11
What is the divisibility by five rule?
Reply:Rule: A number is divisible by v if its concluding digit is a 0 or 5.
See what the rule for divisibility by five has to say about the following number:
Examples of numbers that are divisible by 5 and satisfy this rule
| Number | Explanation |
| ten | Since the last digit is 0, this number is divisible past 5. |
| xv | Since the final digit is five, this number is divisible by five. |
| -45 | Since the last digit is 5, this number is divisible by 5. |
Examples of numbers that are not divisible by 5.
| Number | Explanation |
| one1 | To be divisible past 5, the concluding digit must exist 0 or five. And then eleven fails this test. |
| -19 | To be divisible by v, the concluding digit must be 0 or 5. And then -19 fails this exam. |
- Rules:
- divisible by 2
- by 3
- by iv
- by 5
- by 6
- by 8
- by 9
- by ten
- past eleven
What is the divisibility by 6 rule?
Respond:Since 6 is a multiple of 2 and 3, the rules for divisibility past 6 are a combination of the dominion for two and the rule for three.
In other words, a number passes this divisibility examination just if it passes the testfor 2 and the for 3.
Rule: A number is divisible by half-dozen if it is even and if the sum of its digits is divisible by three.
Examples of numbers that are divisible past six.
| Number | Caption |
| 114 |
|
| 241,122 |
|
See if the following number: is evenly divisible by six.
Examples of numbers that are do non pass this divisibility test.
| Number | Explanation |
| 207 |
|
| 241,124 |
|
- Rules:
- divisible by 2
- by three
- by 4
- by 5
- by 6
- past 8
- by 9
- past 10
- past eleven
Divisibility by 8 Rule
Rule A number passes the examination for 8 if the last iii digits form a number is divisible 8.
Examples of numbers that satisfy this dominion and are divisible past eight.
| Number | Explanation |
| 9,640 | The terminal 3 digits, 640, are divisible by 8. Therefore, ix,640 is divisible eight equally well! |
| -77,184 | The final three digits , 184, are divisible by eight. Therefore, -77,184 is divisible 8 likewise! |
| 20,233,322,496 | The last iii digits, 496, are divisible by 8. Therefore , 20,233,322,496 is divisible 8 equally well! |
Run into what the rule for divisibility by eight has to say nearly the following number:
Examples of numbers that are do non laissez passer this divisibility exam.
| Number | Explanation |
| 9,801 | Since concluding three digits are not divisible past 8, the entire number 9,801 is not. |
| -32,344,588 | Since last 3 digits are not divisible by 8, the unabridged number -32,344,588 is not. |
- Rules:
- divisible by 2
- by iii
- by 4
- by five
- past half-dozen
- past 8
- by ix
- by 10
- by 11
Divisibility past 9 Rule
Rule A number is divisible by ix if the sum of the digits are evenly divisible by 9.
Examples of numbers that satisfy this dominion and are divisible by nine.
| Number | Explanation |
| 4,518 | $$ 4 + 5 + i + viii = 18$$ which is divisible past 9, and then iv,518 is divisible by 9. |
| -vi,993 | $$ vi + nine + nine + 3 = 27 $$ which is divisible by 9 so, the entire number is divisible past 9. |
See if the following number: is evenly divisible by nine.
Examples of numbers that are do not pass this divisibility test.
| Number | Explanation |
| 6,992 | $$ 6 + 9 + 9 + ii = 26 $$ which is not divisible by 9 then, the unabridged number is not divisible by 9. |
| 4,517 | $$ iv + 5 + 1 + seven = 17$$ which is not divisible by ix so, the entire number is not divisible by ix. |
- Rules:
- divisible by 2
- by 3
- past four
- by 5
- by half dozen
- by 8
- by 9
- by 10
- by eleven
Divisibility by 10 Dominion
Rule A number passes the examination for 10 if its last digit is 0
Use the divisibility calculator below to determine if whatever number is divisible by ten. Blazon in whatever number that yous want, and the calculator will utilise the dominion for divisibility by ten to explain the issue.
Examples of numbers that are divisible by 10.
| Number | Explanation |
| xix0 | Last digit is 0, that's all that is needed for a number to exist divisible past 10. |
| -231,110 | Last digit is 0, that'south all that is needed for a number to be divisible by 10. |
See what the rule for divisibility past ten has to say about the post-obit number:
Examples of numbers that do non pass this divisibility test
| Number | Explanation |
| 31,xxfive | Since the last digit is not 0, this number is not divisible by 10. |
| -100,002 | Since the last digit is not 0, this number is not divisible by ten. |
- Rules:
- divisible by 2
- past 3
- past four
- past 5
- by 6
- by eight
- past nine
- past ten
- past xi
Divisibility by 11 Rule
Dominion A number passes the test for xi if the difference of the sums of alternating digits is divisible by 11.(This abstract and confusing sounding rule is much clearer with a few examples).
Utilize the divisibility calculator below to make up one's mind if whatever number is divisible by 11. Type in any number that you want, and the calculator will explain whether or not information technology's divisible by 11 based on this rule.
Run across if the following number: is evenly divisible by 11.
Examples of numbers that satisfy this rule.
| Number | Explanation |
| 1one9,777,6five8 | $$ (1+ nine + vii + half dozen + 8) - (1+ 7 + 7 + 5) = 31 - 20 = 11 $$ and since xi is evenly divisible past 11, the unabridged number is also |
| ten,813 | $$ (1 + 8 + 3) - (0+1) = 12-1 = 11 $$ |
| 25,784 | $$ (2 + seven + 4) - (v + eight) = thirteen - 13 = 0 $$ Yeah, this does indeed work. In case y'all found this one, a fleck disruptive, remember that whatsoever number evenly divides 0. Recall most it, how many 11's are there in 0? None, right. Well that means that 11 divides zero, null times! |
Examples of numbers that do not laissez passer this divisibility examination.
| Number | Caption |
| x,823 | $$ (ane+8+3) - (0+2) = 12- ii =10 $$. No, no practiced. This one fails |
| 35,784 | $$ (iii + 7 + 4) - (5+8) = fourteen - 13 = one $$ |
| 12,347, 496, 132 | $$ (1 + 3 + 7 + 9 + iii) - (two + 4 + 4 + 6 + 3) = 23 - nineteen = 4$$ |
A discussion of caution about Calculators and Big Numbers
Proceed this in mind when you are using a calculator. Calculators lose their accuracy when they start dividing large numbers such every bit 12,347,496,132. Try to divide that big number past eleven. If your calculator outputs that 12,347,496,132 is divisible by eleven, your calculator IS WRONG (Look at the last example at the lesser for details). When yous're dealing with exceedingly large numbers, you should rely, whenever possible, on the rules on this page rather than a computer that can only handle numbers upwardly to a certain size..
Source: https://www.mathwarehouse.com/arithmetic/numbers/divisibility-rules-and-tests.php
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