Answer :

To determine if [tex]\( 5,124,114 \)[/tex] is divisible by 6, we need to check two things:

1. Whether the number is divisible by 2.
2. Whether the number is divisible by 3.

### Step 1: Check Divisibility by 2
A number is divisible by 2 if its last digit is even. The last digit of [tex]\( 5,124,114 \)[/tex] is 4, which is even. Hence, [tex]\( 5,124,114 \)[/tex] 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 find the sum of the digits:
- The digits of [tex]\( 5,124,114 \)[/tex] are: 5, 1, 2, 4, 1, 1, 4.
- Adding these digits: [tex]\( 5 + 1 + 2 + 4 + 1 + 1 + 4 = 18 \)[/tex].

Now, we check if 18 is divisible by 3:
- [tex]\( 18 \div 3 = 6 \)[/tex] (which is an integer).

Since 18 is divisible by 3, [tex]\( 5,124,114 \)[/tex] is also divisible by 3.

### Conclusion: Divisibility by 6
A number is divisible by 6 if and only if it is divisible by both 2 and 3.

Since [tex]\( 5,124,114 \)[/tex] is divisible by both 2 and 3, we can conclude that:
- [tex]\( 5,124,114 \)[/tex] is divisible by 6.

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