Q. Without dividing, determine if 91,626 is divisible by 6 and explain how you know.91,626□ divisible by 6
Check Even Number: To determine if a number is divisible by 6, it must be divisible by both 2 and 3. For a number to be divisible by 2, it must be even, which means its last digit must be 0, 2, 4, 6, or 8. Let's check if 91,626 is even.
Add Digits: The last digit of 91,626 is 6, which is an even number. Therefore, 91,626 is divisible by 2.
Check Divisibility by 3: Next, to check if a number is divisible by 3, we add up all the digits in the number and see if the sum is divisible by 3. Let's add up the digits of 91,626: 9+1+6+2+6.
Calculate Sum: The sum of the digits is 9+1+6+2+6=24. Now we need to determine if 24 is divisible by 3.
Divisibility by 3: Since 24 is divisible by 3 (as 24÷3=8), the sum of the digits of 91,626 is divisible by 3. Therefore, 91,626 is divisible by 3.
Conclusion: Since 91,626 is divisible by both 2 and 3, we can conclude that 91,626 is divisible by 6.