Is 6 a factor of 54c+48?
To determine if 6 is a factor of 54c+48, we need to check if 54c+48 is evenly divisible by 6.
We know that a number is divisible by 6 if it is divisible by both 2 and 3.
First, let's check if 54c+48 is divisible by 2. Since 48 is even, we know that it is divisible by 2. Therefore, 54c+48 is divisible by 2 if 54c is also divisible by 2. To determine if 54c is divisible by 2, we need to check if c is an even number. If c is even, then 54c is divisible by 2.
Next, let's check if 54c+48 is divisible by 3. To determine if a number is divisible by 3, we need to check if the sum of its digits is divisible by 3. In this case, the sum of the digits is 5+4+c+4+8 = 21+c. For 21+c to be divisible by 3, c must be 2, 5, or 8.
In conclusion, 6 is a factor of 54c+48 if c is an even number and the sum of the digits of 54c+48 is divisible by 3.