Find the least value of x for which the number 57x716 is divisible by 9.

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Accepted Answer

A number is divisible by 9 if the sum of its digits is divisible by 9.

Given number: 57x716
Sum of digits = 5 + 7 + x + 7 + 1 + 6 = 26 + x

We want 26 + x to be divisible by 9.

The multiples of 9 near 26 are 18, 27, 36, ...

Since 26 + x ≥ 26, the next multiple of 9 after 26 is 27.

So, 26 + x = 27
=> x = 27 - 26 = 1

But 1 is an option, let's check if x=1 makes the number divisible by 9.

Sum = 26 + 1 = 27, which is divisible by 9.

Wait, the options include 1 and 0. Let's check x=0:
Sum = 26 + 0 = 26, which is not divisible by 9.

So the least value of x is 1.

Therefore, the correct answer is 1.

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