Which of the following numbers divides 545714151?

The correct answer is Option 3: 3.

To determine which of the given numbers (10, 6, 7, or 3) divides 545,714,151, we can apply divisibility rules to test each option efficiently.

Step 1: Test for divisibility by 10
A number is divisible by 10 if its last digit is 0. The last digit of 545,714,151 is 1, so it is not divisible by 10.

Step 2: Test for divisibility by 3
A number is divisible by 3 if the sum of all its digits is divisible by 3.
Let us calculate the sum of the digits of 545,714,151:

$\text{Sum of digits}=5+4+5+7+1+4+1+5+1$

$\text{Sum of digits}=33$

Now, check if 33 is divisible by 3:

$33÷3=11$

Since 33 is completely divisible by 3, the original number 545,714,151 is also divisible by 3.

Step 3: Verify other options
- A number is divisible by 6 if it is divisible by both 2 and 3. Since 545,714,151 is an odd number (ends in 1), it is not divisible by 2, and therefore not divisible by 6.
- Since we have already confirmed divisibility by 3, option 3 is clearly correct.

Therefore, 3 divides 545,714,151.