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Prove if a number is divisible by 3 then the sum of its digits must also be divisible by 3?
Wiki User
∙ 9y ago
Suppose an (n+1)-digit number, X, is divisible by 3.
Let X = a0*100 + a1*101 + a2*102 + ... + an*10n
= a0 + a1*(1+9) + a2*(1+99) + ... + an*(1+999..9)
= [a0 + a1 + a2 + ... + an] + [a1*9 + a2*99 + ... + an*999..9]
3 divides 9, 99, 999, etc so 3 divides each term in the second brackets (parentheses). Therefore 3 must divide the sum in the first brackets. That is, 3 must divide the sum of digits.
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∙ 9y ago
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Is the number 5886 divisible by 9?
Yes it is. In order for it to be divisible by 9, the sum of the digits in the number must also be divisible by 9. In this case - the sum of the digits is 27.
If the sum of the digit is divisible by 3 the number is divisible by?
That means the number itself is divisible by three. the sum of the digits in 144, for example, is 9. 144 divided by 3 is 48. The sum of the digits in 21 is 3. 21 divided by 3 is 7.If the number is an even number and the sum of the digits is divisible by 3, the number is also divisible by 6. 144 is even and the sum of the digits is divisible by 3, so 144 is also divisible by 6. 144/6 = 24. And finally, if the sum is divisible by 9, the number itself is also divisible by 9. 27 is an example of this.
What largest 3 - digit number divisible by both 6 and 9?
999 is divisible by 9, but not by six; the next lower number divisible by 9 is 990, which is also divisible by 6, so that's the answer. Some shortcuts for divisibility: 0 is divisible by any number. If the last digit of a number is divisible by 2, the number itself is divisible by 2. If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3. If the last TWO digits of a number are divisible by 4, the number itself is divisible by 4. If the last digit of a number is divisible by 5, the number itself is divisible by 5. If a number is divisible by both 2 and 3, it is divisible by 6. If the last THREE digits of a number are divisible by 8, the number itself is divisible by 8. If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9. 990: 9+9+0=18, which is divisible by 9, so 990 is divisible by 9. 18 is also divisible by 3, so 990 is divisible by 3, and since 990 ends in 0 it's also divisible by 2, meaning that it's divisible by 6 as well.
What are the numbers that are divisible by 4?
In order for a number to be divisible by 4, it has to be even.As every multiple of 100 is divisible by 4, we only have to look at the rightmost two digits.If the number consisting of these digits is divisible by 4, then the original number is also divisible by 4.For example:353 is odd, therefore is not divisible by 4.1284 - We'll look at the rightmost digits giving us 84, which is divisible by 4, so 1284 is also divisible by 4.258 - The two rightmost digits give us 58, which is not divisible by 4. Hence 258 is also not divisible by 4.
Is 5278 divisible by3?
Add up the digits---5+2+7+8 22 which is NOT a multiple of 3 so it is NOT divisible by 3. == Here is a list of the divisibility rules: 2 If the last digit is even, the number is divisible by 2. 3 If the sum of the digits is divisible by 3, the number is also. 4 If the last two digits form a number divisible by 4, the number is also. 5 If the last digit is a 5 or a 0, the number is divisible by 5. 6 If the number is divisible by both 3 and 2, it is also divisible by 6. 7Take the last digit, double it, and subtract it from the rest of the number;if the answer is divisible by 7 (including 0), then the number is also. 8If the last three digits form a number divisible by 8,then so is the whole number. 9 If the sum of the digits is divisible by 9, the number is also. 10 If the number ends in 0, it is divisible by 10. 11 Alternately add and subtract the digits from left to right. (You can think of the first digit as being 'added' to zero.)If the result (including 0) is divisible by 11, the number is also.Example: to see whether 365167484 is divisible by 11, start by subtracting:[0+]3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11. 12 If the number is divisible by both 3 and 4, it is also divisible by 12. 13Delete the last digit from the number, then subtract 9 times the deleteddigit from the remaining number. If what is left is divisible by 13,then so is the original number
Is 1 trillion 17 a prime number?
Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.Since the sum of the digits is divisible by 3, the original number is also divisible by 3.
Is the number 5886 divisible by 9?
Yes it is. In order for it to be divisible by 9, the sum of the digits in the number must also be divisible by 9. In this case - the sum of the digits is 27.
If the sum of the digits is divisible by9 that number is also divisible by?
3 and 9
If the ............. of the digits for a whole number is divisible by three then the whole number is also divisible by three?
You would fill in the blank with the word sum, which means that you add each of the digits of the number. If that sum is divisible by three then the number is divisible by 3.
Is 2681 divisible by 9?
No it's not. For a number to be divisible by 9, the sumof the digits must also be divisible by 9. These digits add up to 17
If the sum of the digit is divisible by 3 the number is divisible by?
That means the number itself is divisible by three. the sum of the digits in 144, for example, is 9. 144 divided by 3 is 48. The sum of the digits in 21 is 3. 21 divided by 3 is 7.If the number is an even number and the sum of the digits is divisible by 3, the number is also divisible by 6. 144 is even and the sum of the digits is divisible by 3, so 144 is also divisible by 6. 144/6 = 24. And finally, if the sum is divisible by 9, the number itself is also divisible by 9. 27 is an example of this.
The two leading digits of each 4-digit number are not shown which number is divisible by 4?
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What largest 3 - digit number divisible by both 6 and 9?
999 is divisible by 9, but not by six; the next lower number divisible by 9 is 990, which is also divisible by 6, so that's the answer. Some shortcuts for divisibility: 0 is divisible by any number. If the last digit of a number is divisible by 2, the number itself is divisible by 2. If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3. If the last TWO digits of a number are divisible by 4, the number itself is divisible by 4. If the last digit of a number is divisible by 5, the number itself is divisible by 5. If a number is divisible by both 2 and 3, it is divisible by 6. If the last THREE digits of a number are divisible by 8, the number itself is divisible by 8. If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9. 990: 9+9+0=18, which is divisible by 9, so 990 is divisible by 9. 18 is also divisible by 3, so 990 is divisible by 3, and since 990 ends in 0 it's also divisible by 2, meaning that it's divisible by 6 as well.
What are the rules of the divisibility?
1- Any number is divisible by 1. 2- Any even number is divisible by 2. 3- If its digits add up to a number divisible by 3, the whole number is divisible by 3. 4- If the last two digits are divisible by 4, the whole number is divisible by 4. 5- If it ends in 5 or 0, the whole number is divisible by 5. 6- If it's even and also divisible by 3, the whole number is divisible by 6. 7- There is no rule for 7. 8- If the last three digits are divisible by 8, the whole number is divisible by 8. 9- If its digits add up to a number divisible by 9, the whole number is divisible by 9. 10- If it ends in 0, the whole number is divisible by 10.
What are the numbers that are divisible by 4?
In order for a number to be divisible by 4, it has to be even.As every multiple of 100 is divisible by 4, we only have to look at the rightmost two digits.If the number consisting of these digits is divisible by 4, then the original number is also divisible by 4.For example:353 is odd, therefore is not divisible by 4.1284 - We'll look at the rightmost digits giving us 84, which is divisible by 4, so 1284 is also divisible by 4.258 - The two rightmost digits give us 58, which is not divisible by 4. Hence 258 is also not divisible by 4.
Is 24207 divisible by 9?
Nope - in order for a number to be divisible by 9, the sum of its digits must also be divisible by 9. In this case, the digits 2+4+2+7=15.
Is 5278 divisible by3?
Add up the digits---5+2+7+8 22 which is NOT a multiple of 3 so it is NOT divisible by 3. == Here is a list of the divisibility rules: 2 If the last digit is even, the number is divisible by 2. 3 If the sum of the digits is divisible by 3, the number is also. 4 If the last two digits form a number divisible by 4, the number is also. 5 If the last digit is a 5 or a 0, the number is divisible by 5. 6 If the number is divisible by both 3 and 2, it is also divisible by 6. 7Take the last digit, double it, and subtract it from the rest of the number;if the answer is divisible by 7 (including 0), then the number is also. 8If the last three digits form a number divisible by 8,then so is the whole number. 9 If the sum of the digits is divisible by 9, the number is also. 10 If the number ends in 0, it is divisible by 10. 11 Alternately add and subtract the digits from left to right. (You can think of the first digit as being 'added' to zero.)If the result (including 0) is divisible by 11, the number is also.Example: to see whether 365167484 is divisible by 11, start by subtracting:[0+]3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11. 12 If the number is divisible by both 3 and 4, it is also divisible by 12. 13Delete the last digit from the number, then subtract 9 times the deleteddigit from the remaining number. If what is left is divisible by 13,then so is the original number
