A number is divisible by if the sum of its digits is a multiple of .
A number is divisible by if it is even and also a multiple of .
A number is divisible by if the sum of its digits is a multiple of .
Will a number divisible by 6 necessarily be divisible by 3?
Wow! What a pleasant and entertaining topic! In this article, we will teach you how to identify if a number is divisible by , and , in a matter of seconds!
Shall we start?
A number is divisible by if the sum of its digits is a multiple of .
If the sum of the digits of the number is not a multiple of , neither will the original number be.
Will a number divisible by 6 necessarily be divisible by 2?
Determine if the following number is divisible by 3:
\( 132 \)
Determine if the following number is divisible by 3:
\( 352 \)
The number
How will we know if it is divisible by ? In a very simple way, we will calculate the sum of its digits:
We already know that is divisible by , therefore, is as well.
Note: we recommend adding the digits one more step to avoid errors.
That is, if after adding the digits the result is , we can add the new digits obtained again.
This sum will give us a smaller number and, in this way, we can be sure whether it is a multiple of or not.
In the same way, we will know that, if the number obtained in the result is a multiple of , the original one is as well.
Is the number divisible by ?
Solution: Let's check the sum of its digits:
–> The result is, indeed, a number divisible by , therefore, the original is as well.
Note: We could have continued and added the digits to arrive at a smaller number.
is divisible by . Therefore, is also divisible by .
Is the number divisible by ?
Solution:
is divisible by , therefore, is divisible by .
Determine if the following number is divisible by 3:
\( 673 \)
Determine if the following number is divisible by 3:
\( 564 \)
Will a number divisible by 9 necessarily be divisible by 6?
Is the number divisible by ?
Solution:
is not divisible by , therefore, is not divisible by .
A number is divisible by if it is even and also a multiple of .
In fact, we must check the conditions:
If both conditions are met, the number is divisible by .
Will a number divisible by 3 necessarily be divisible by 6?
Will a number divisible by 9 necessarily be divisible by 3?
Will a number divisible by 3 necessarily be divisible by 9?
Is the number divisible by ?
Solution:
Let's see if the number is even.
Yes, the number is even. The units digit is and is an even number.
Let's continue with the second condition -> Is the number divisible by ?
Let's calculate the sum of its digits:
is divisible by , therefore, is also divisible by .
Both conditions are met, so is divisible by .
Is the number divisible by ?
Solution:
Let's see if the number is even:
The units digit is , is odd, therefore, the number is not divisible by .
Even if only one of the conditions is not met, that is enough to determine that the number is not divisible by .
Will a number divisible by 2 necessarily be divisible by 6?
Is the number below divisible by 9?
\( 189 \)
Is the number below divisible by 9?
\( 987 \)
A number is divisible by if the sum of its digits is a multiple of .
If the sum of the digits of the number is not a multiple of , then the original number will not be either.
Note: After adding the digits once and obtaining some number as a result, it is advisable to also add the digits of this last number to arrive at a smaller number that makes it easier to check if it is a multiple of .
The number
Solution :
Let's add its digits
is divisible by and at this stage, we can determine that is divisible by .
If you still doubt that is divisible by , you can add the digits of the result obtained again:
is divisible by , therefore, is divisible by .
Is the number below divisible by 9?
\( 685 \)
Is the number below divisible by 9?
\( 999 \)
Will a number divisible by 6 necessarily be divisible by 3?
Is the number divisible by ?
Solution :
is not divisible by , therefore, is divisible by .
Is the number divisible by ?
Solution:
is divisible by , therefore, is divisible by .
Will a number divisible by 6 necessarily be divisible by 2?
Yes
Determine if the following number is divisible by 3:
Yes
Determine if the following number is divisible by 3:
No
Determine if the following number is divisible by 3:
No
Determine if the following number is divisible by 3:
Yes
Will a number divisible by 6 necessarily be divisible by 2?
Determine if the following number is divisible by 3:
\( 132 \)
Determine if the following number is divisible by 3:
\( 352 \)