To determine if 58,812 is divisible by 6 without directly dividing, we need to use the rules of divisibility for 6. A number is divisible by 6 if and only if it is divisible by both 2 and 3. Let's check each condition step-by-step.
### Step 1: Check Divisibility by 2
A number is divisible by 2 if its last digit is even. Let’s examine the last digit of 58,812:
- The last digit is 2, which is even.
Therefore, 58,812 is divisible by 2.
### Step 2: Check Divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3. Let’s calculate the sum of the digits of 58,812:
- The digits are: 5, 8, 8, 1, and 2.
- Summing them up: [tex]\( 5 + 8 + 8 + 1 + 2 = 24 \)[/tex]
Now we need to check if 24 is divisible by 3:
- 24 divided by 3 is exactly 8, which means 24 is divisible by 3.
### Step 3: Confirm Divisibility by 6
Since 58,812 is divisible by 2 and the sum of its digits (24) is divisible by 3, we can conclude that 58,812 is divisible by 6.
### Conclusion
Therefore, without directly dividing, we can determine that 58,812 is divisible by 6 based on divisibility rules for 2 and 3.
