Solved on Dec 14, 2023

Find the value of $x$ that makes $4 \mid 8473x$ true, where $\mid$ represents divisibility.

STEP 1

Assumptions
1. We are looking for a digit $x$ such that $8473x$ is divisible by $4$ .
2. A number is divisible by $4$ if the number formed by its last two digits is divisible by $4$ .

STEP 2

Since we are only concerned with the divisibility of $8473x$ by $4$ , we need to focus on the last two digits of the number, which are $3x$ .

STEP 3

The divisibility rule for $4$ states that if the last two digits of a number form a number that is divisible by $4$ , then the entire number is divisible by $4$ .

STEP 4

We need to find a digit $x$ such that the two-digit number $3x$ is divisible by $4$ .

STEP 5

List all two-digit multiples of $4$ that start with $3$ to find the possible values of $x$ .

STEP 6

The two-digit multiples of $4$ that start with $3$ are $32$ , $36$ , and $40$ (note that $40$ is not considered since it is not a two-digit number with $3$ as the tens place).

STEP 7

From the multiples listed in STEP_6, we can see that the possible values for $x$ are $2$ and $6$ .

STEP 8

Therefore, the values of $x$ that make $8473x$ divisible by $4$ are $2$ and $6$ .
The value of $x$ for the last digits that makes $4 \mid 8473x$ a true statement can be either $2$ or $6$ .

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Find the value of $x$ that makes $4 \mid 8473x$ true, where $\mid$ represents divisibility.

STEP 1

Assumptions
1. We are looking for a digit $x$ such that $8473x$ is divisible by $4$ .
2. A number is divisible by $4$ if the number formed by its last two digits is divisible by $4$ .

STEP 2

Since we are only concerned with the divisibility of $8473x$ by $4$ , we need to focus on the last two digits of the number, which are $3x$ .

STEP 3

The divisibility rule for $4$ states that if the last two digits of a number form a number that is divisible by $4$ , then the entire number is divisible by $4$ .

STEP 4

We need to find a digit $x$ such that the two-digit number $3x$ is divisible by $4$ .

STEP 5

List all two-digit multiples of $4$ that start with $3$ to find the possible values of $x$ .

STEP 6

The two-digit multiples of $4$ that start with $3$ are $32$ , $36$ , and $40$ (note that $40$ is not considered since it is not a two-digit number with $3$ as the tens place).

STEP 7

From the multiples listed in STEP_6, we can see that the possible values for $x$ are $2$ and $6$ .

STEP 8

Therefore, the values of $x$ that make $8473x$ divisible by $4$ are $2$ and $6$ .
The value of $x$ for the last digits that makes $4 \mid 8473x$ a true statement can be either $2$ or $6$ .

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Find the value of xxx that makes 4∣8473x4 \mid 8473x4∣8473x true, where ∣\mid∣ represents divisibility.

STEP 1

Assumptions1. We are looking for a digit xxx such that 8473x8473x8473x is divisible by 444.2. A number is divisible by 444 if the number formed by its last two digits is divisible by 444.

STEP 2

Since we are only concerned with the divisibility of 8473x8473x8473x by 444, we need to focus on the last two digits of the number, which are 3x3x3x.

STEP 3

The divisibility rule for 444 states that if the last two digits of a number form a number that is divisible by 444, then the entire number is divisible by 444.

STEP 4

We need to find a digit xxx such that the two-digit number 3x3x3x is divisible by 444.

STEP 5

List all two-digit multiples of 444 that start with 333 to find the possible values of xxx.

STEP 6

The two-digit multiples of 444 that start with 333 are 323232, 363636, and 404040 (note that 404040 is not considered since it is not a two-digit number with 333 as the tens place).

STEP 7

From the multiples listed in STEP_6, we can see that the possible values for xxx are 222 and 666.

STEP 8

Therefore, the values of xxx that make 8473x8473x8473x divisible by 444 are 222 and 666.The value of xxx for the last digits that makes 4∣8473x4 \mid 8473x4∣8473x a true statement can be either 222 or 666.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ that makes $4 \mid 8473x$ true, where $\mid$ represents divisibility.

Assumptions
1. We are looking for a digit $x$ such that $8473x$ is divisible by $4$ .
2. A number is divisible by $4$ if the number formed by its last two digits is divisible by $4$ .

Since we are only concerned with the divisibility of $8473x$ by $4$ , we need to focus on the last two digits of the number, which are $3x$ .

The divisibility rule for $4$ states that if the last two digits of a number form a number that is divisible by $4$ , then the entire number is divisible by $4$ .

We need to find a digit $x$ such that the two-digit number $3x$ is divisible by $4$ .

List all two-digit multiples of $4$ that start with $3$ to find the possible values of $x$ .

The two-digit multiples of $4$ that start with $3$ are $32$ , $36$ , and $40$ (note that $40$ is not considered since it is not a two-digit number with $3$ as the tens place).

From the multiples listed in STEP_6, we can see that the possible values for $x$ are $2$ and $6$ .

Therefore, the values of $x$ that make $8473x$ divisible by $4$ are $2$ and $6$ .
The value of $x$ for the last digits that makes $4 \mid 8473x$ a true statement can be either $2$ or $6$ .