What least value must be assigned to ' * ' so that the numbers 451 * 603 is exactly divisible by 9?
8
A number is divisible by 9 if the sum of its digits is divisible by 9. Let's denote the missing digit as 'x'. The given number is 451x603. To check for divisibility by 9, we sum the digits:
4 + 5 + 1 + x + 6 + 0 + 3 = 19 + x
Now, we need to find the smallest value of x such that (19 + x) is divisible by 9. Let's test values:
- If x = 0, 19 + 0 = 19 (not divisible by 9)
- If x = 1, 19 + 1 = 20 (not divisible by 9)
- If x = 2, 19 + 2 = 21 (not divisible by 9)
- If x = 3, 19 + 3 = 22 (not divisible by 9)
- If x = 4, 19 + 4 = 23 (not divisible by 9)
- If x = 5, 19 + 5 = 24 (not divisible by 9)
- If x = 6, 19 + 6 = 25 (not divisible by 9)
- If x = 7, 19 + 7 = 26 (not divisible by 9)
- If x = 8, 19 + 8 = 27 (divisible by 9)
Therefore, the least value that must be assigned to '*' is 8, making the number 4518603. The sum of its digits (4 + 5 + 1 + 8 + 6 + 0 + 3 = 27) is divisible by 9. This confirms that 4518603 is divisible by 9.
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select the correct answer using the code given below:
