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
Determine if the following number is divisible by 3:
\( 352 \)
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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