If the six-digit number 45231x is completely divisible by 9, what is the value of the digi… — State PSC Exam

If the six-digit number $45231x$ is completely divisible by $9$ , what is the value of the digit $x$ ?

Answer: 3

According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is a multiple of 9. For the number

45231x

, the sum of the digits is

4 + 5 + 2 + 3 + 1 + x = 15 + x

. The smallest multiple of 9 that is greater than or equal to 15 is 18. Setting

15 + x = 18

gives

x = 3

Find the sum of the known digits in the given number.

4 + 5 + 2 + 3 + 1 = 15

The divisibility rule for 9 requires analyzing the sum of all digits.

Formulate the condition for divisibility by 9.

15 + x

must be a multiple of 9.

Including the unknown unit digit

x

, the total digit sum is

15 + x

Solve for the single-digit integer

x

where

0 \le x \le 9

x = 3

The smallest multiple of 9 greater than or equal to 15 is 18, giving

15 + x = 18

, so

x = 3

Divisibility Rule for 9

Dividing 452,310 by 9 yields 50,256 with a remainder of 6. To make the number divisible by 9, the remaining amount needed is

9 - 6 = 3

, so the unit digit

x

must be 3.

Estimated Time:45s

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