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 .
Determine if the following number is divisible by 3:
\( 564 \)
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.
Determine if the following number is divisible by 3:
\( 673 \)
Determine if the following number is divisible by 3:
\( 352 \)
Determine if the following number is divisible by 3:
\( 132 \)
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:
โ> 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 .
Will a number divisible by 6 necessarily be divisible by 2?
Will a number divisible by 6 necessarily be divisible by 3?
Is the number below divisible by 9?
\( 999 \)
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 .
Is the number below divisible by 9?
\( 685 \)
Is the number below divisible by 9?
\( 987 \)
Is the number below divisible by 9?
\( 189 \)
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?
Will a number divisible by 3 necessarily be divisible by 9?
Will a number divisible by 9 necessarily be divisible by 3?
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 .
Will a number divisible by 3 necessarily be divisible by 6?
Will a number divisible by 9 necessarily be divisible by 6?
Determine if the following number is divisible by 3:
\( 564 \)
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 .
Determine if the following number is divisible by 3:
To determine if the number 564 is divisible by 3, we apply the divisibility rule for 3:
Let's calculate the sum of the digits of 564:
Next, we check if 15 is divisible by 3. Since 15 can be divided by 3 without a remainder, it is divisible by 3:
Therefore, based on the divisibility rule, 564 is divisible by 3.
Thus, the correct answer is Yes.
Yes
Determine if the following number is divisible by 3:
To determine if 673 is divisible by 3, we must use the divisibility rule for 3, which states that a number is divisible by 3 if the sum of its digits is divisible by 3.
First, we'll calculate the sum of the digits: .
Calculating this, we get: .
Next, we check if 16 is divisible by 3. Dividing 16 by 3 gives a quotient of 5 and a remainder of 1.
Since 16 is not divisible by 3 (as it leaves a remainder), we conclude that 673 is not divisible by 3.
Thus, the correct answer is No.
No
Determine if the following number is divisible by 3:
To determine if 352 is divisible by 3, we need to follow these steps:
Let's work through the procedure:
The number consists of the digits 3, 5, and 2.
Step 1: Calculate the sum of the digits.
The sum is .
Step 2: Check if 10 is divisible by 3.
Since 10 divided by 3 gives a remainder, 10 is not divisible by 3.
Therefore, the number 352 is not divisible by 3.
The correct answer is No.
No
Determine if the following number is divisible by 3:
To determine if the number is divisible by , we can apply the rule for divisibility by , which involves summing the digits of the number.
Step-by-step solution:
Since the sum of the digits is and is divisible by , the number is also divisible by .
Therefore, the number is divisible by , and the correct choice is:
Yes
Yes
Will a number divisible by 6 necessarily be divisible by 2?
In order to determine if a number divisible by 6 is also divisible by 2, we first review the divisibility rules:
Consider a number that is divisible by 6. By definition, since 6 itself factors into 2 multiplied by 3, any number divisible by 6 must be divisible by 2 and 3. This means that any number divisible by 6 is automatically divisible by 2 because 2 is a part of its factorization.
Therefore, yes, any number divisible by 6 will necessarily be divisible by 2 as per the rule of divisibility.
Thus, the correct choice is:
This conclusion adheres strictly to divisibility rules and confirms the assertion that being divisible by 6 includes being divisible by 2.
Yes
Determine if the following number is divisible by 3:
\( 673 \)
Determine if the following number is divisible by 3:
\( 352 \)
Determine if the following number is divisible by 3:
\( 132 \)