Determine if the following number is divisible by 6:
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Determine if the following number is divisible by 6:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Check divisibility by 2.
The last digit of 876 is 6, which is an even number. Thus, 876 is divisible by 2.
Step 2: Check divisibility by 3.
The sum of the digits is .
Check if 21 is divisible by 3: divide , which is a whole number. Thus, 21 is divisible by 3, so 876 is also divisible by 3.
Step 3: Conclude divisibility by 6.
Since 876 is divisible by both 2 and 3, it is also divisible by 6.
Therefore, the number 876 is divisible by 6, and the answer to the problem is Yes.
Yes
Will a number divisible by 6 necessarily be divisible by 3?
You can, but divisibility rules are faster and prevent errors! Checking if the last digit is even and if digit sum is divisible by 3 takes seconds, while long division takes much longer.
Keep applying the rule! Since with no remainder, 21 is divisible by 3. You can also add again: , and 3 is clearly divisible by 3.
Yes, always check both! A number must be divisible by both 2 and 3 to be divisible by 6. Missing either test gives you incomplete information.
Any composite number! For example, to check divisibility by 12, test divisibility by both 3 and 4. The key is breaking down the number into its prime factors.
Numbers ending in 0 are automatically divisible by 2 (since 0 is even). You still need to check the digit sum rule for 3 to confirm divisibility by 6.
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