Divisibility Analysis for 386937355

The question asks us to identify which of the given numbers (3, 15, 5, 14) divides the number 386937355 without leaving a remainder. We can determine this by applying the divisibility rules for each number.

Understanding Divisibility Rules

Let's review the rules we'll use:

• Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
• Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
• Divisibility by 14: A number is divisible by 14 if it is divisible by both 2 and 7.
• Divisibility by 15: A number is divisible by 15 if it is divisible by both 3 and 5.

Applying the Rules to 386937355

Testing Divisibility by 3

First, we sum the digits of 386937355:

Sum = $3 + 8 + 6 + 9 + 3 + 7 + 3 + 5 + 5 = 49$.

Now, we check if the sum (49) is divisible by 3.

$49 \div 3 = 16$ with a remainder of 1.

Since the sum of the digits is not divisible by 3, the number 386937355 is not divisible by 3.

Testing Divisibility by 5

We look at the last digit of 386937355.

The last digit is 5.

According to the rule, if the last digit is 0 or 5, the number is divisible by 5. Therefore, 386937355 is divisible by 5.

Testing Divisibility by 14

For a number to be divisible by 14, it must be divisible by both 2 and 7.

Check for Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8). The last digit of 386937355 is 5, which is odd. So, 386937355 is not divisible by 2.

Since 386937355 is not divisible by 2, it cannot be divisible by 14, regardless of whether it's divisible by 7.

Testing Divisibility by 15

For a number to be divisible by 15, it must be divisible by both 3 and 5.

From our previous checks:

• 386937355 is divisible by 5.
• 386937355 is not divisible by 3.

Since it fails the divisibility test for 3, the number 386937355 is not divisible by 15.

Conclusion

By applying the standard divisibility rules, we found the following:

• 386937355 is not divisible by 3.
• 386937355 is divisible by 5.
• 386937355 is not divisible by 14.
• 386937355 is not divisible by 15.

Therefore, the only number among the choices provided that divides 386937355 is 5.