Determine if the following number is divisible by 3:
We have hundreds of course questions with personalized recommendations + Account 100% premium
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:
\( 564 \)
This works because of how our base-10 number system relates to multiples of 3. When you add digits, you're essentially checking if the number leaves the same remainder when divided by 3!
Keep adding! For example, if digits sum to 27, add again: . Since 9 is divisible by 3, the original number is too. Repeat until you get a single digit.
Yes! The digit sum rule works for 3, 6, and 9. For 6, the number must be divisible by both 2 (even) and 3 (digit sum divisible by 3).
Think of multiples of 3: 3, 6, 9, 12, 15, 18... Since 16 falls between 15 and 18, it's not a multiple of 3. Or divide: 16 ÷ 3 = 5 remainder 1.
Absolutely! This is why the digit sum rule is so powerful. Whether the number has 3 digits or 300 digits, just add all the digits together and test that much smaller sum.
Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime