Master divisibility rules for 3, 6, and 9 with step-by-step examples and practice problems. Learn digit sum tricks and shortcuts for quick mental math.
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 .
Is the number below divisible by 9?
\( 987 \)
Will a number divisible by 6 necessarily be divisible by 3?
To determine whether a number divisible by 6 is necessarily divisible by 3, we need to understand the properties of divisibility for the numbers involved.
Let's analyze the problem step by step:
Therefore, the answer to the problem is Yes.
Answer:
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.
Answer:
Yes
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
Answer:
Yes
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.
Answer:
No
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.
Answer:
No