Type a digit that makes this statement true. 2,497,97_ is divisible by 6.
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Type a digit that makes this statement true. 2,497,97_ is divisible by 6.
To determine what digit can replace the underscore in 2,497,97_ so that the number is divisible by 6, we first need to know that a number is divisible by 6 if it is divisible by both 2 and 3.
1. Divisibility by 2: The last digit (the digit we’re replacing with “_”) must be even. Possible even digits are 0, 2, 4, 6, or 8.
2. Divisibility by 3: To check for divisibility by 3, the sum of the digits must be divisible by 3. The current sum of the digits is:
( 2 + 4 + 9 + 7 + 9 = 31 )
Now add the digit (let’s call it x):
( 31 + x )
We want ( 31 + x ) to be divisible by 3. The remainders of 31 when divided by 3 is 1 (since ( 31 div 3 = 10 ) remainder ( 1 )). Therefore, we need ( x ) to be 2 (because 1 + 2 = 3, which is divisible by 3).
Now, we check:
– x = 0: ( 31 + 0 = 31 ) (not divisible by 3)
– x = 2: ( 31 +