Solved on Jan 18, 2024

Which number is a multiple of 4, 5, and 20? $10$ is a multiple of 4, 5, and 20.

STEP 1

Assumptions
1. We need to determine which of the given statements is true regarding the number 10 being a multiple of another number.

STEP 2

Define what it means for one number to be a multiple of another.
$A \text{ is a multiple of } B \text{ if there exists an integer } n \text{ such that } A = n \times B.$

STEP 3

Check if 10 is a multiple of 4.
To be a multiple of 4, there must be an integer $n$ such that $10 = n \times 4$ .

STEP 4

Attempt to find an integer $n$ that satisfies $10 = n \times 4$ .
Since $10 \div 4 = 2.5$ and 2.5 is not an integer, there is no integer $n$ that satisfies the equation.

STEP 5

Conclude that 10 is not a multiple of 4.

STEP 6

Check if 10 is a multiple of 5.
To be a multiple of 5, there must be an integer $n$ such that $10 = n \times 5$ .

STEP 7

Attempt to find an integer $n$ that satisfies $10 = n \times 5$ .
Since $10 \div 5 = 2$ and 2 is an integer, there is an integer $n$ that satisfies the equation.

STEP 8

Conclude that 10 is a multiple of 5.

STEP 9

Check if 10 is a multiple of 20.
To be a multiple of 20, there must be an integer $n$ such that $10 = n \times 20$ .

STEP 10

Attempt to find an integer $n$ that satisfies $10 = n \times 20$ .
Since $10 \div 20 = 0.5$ and 0.5 is not an integer, there is no integer $n$ that satisfies the equation.

STEP 11

Conclude that 10 is not a multiple of 20.

STEP 12

Check if 10 is a multiple of 25.
To be a multiple of 25, there must be an integer $n$ such that $10 = n \times 25$ .

STEP 13

Attempt to find an integer $n$ that satisfies $10 = n \times 25$ .
Since $10 \div 25 = 0.4$ and 0.4 is not an integer, there is no integer $n$ that satisfies the equation.

STEP 14

Conclude that 10 is not a multiple of 25.

STEP 15

Determine the true statement.
Based on the calculations, the only true statement is "10 is a multiple of 5."
The correct answer is: 10 is a multiple of 5.

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Which number is a multiple of 4, 5, and 20? $10$ is a multiple of 4, 5, and 20.

STEP 1

Assumptions
1. We need to determine which of the given statements is true regarding the number 10 being a multiple of another number.

STEP 2

Define what it means for one number to be a multiple of another.
$A \text{ is a multiple of } B \text{ if there exists an integer } n \text{ such that } A = n \times B.$

STEP 3

Check if 10 is a multiple of 4.
To be a multiple of 4, there must be an integer $n$ such that $10 = n \times 4$ .

STEP 4

Attempt to find an integer $n$ that satisfies $10 = n \times 4$ .
Since $10 \div 4 = 2.5$ and 2.5 is not an integer, there is no integer $n$ that satisfies the equation.

STEP 5

Conclude that 10 is not a multiple of 4.

STEP 6

Check if 10 is a multiple of 5.
To be a multiple of 5, there must be an integer $n$ such that $10 = n \times 5$ .

STEP 7

Attempt to find an integer $n$ that satisfies $10 = n \times 5$ .
Since $10 \div 5 = 2$ and 2 is an integer, there is an integer $n$ that satisfies the equation.

STEP 8

Conclude that 10 is a multiple of 5.

STEP 9

Check if 10 is a multiple of 20.
To be a multiple of 20, there must be an integer $n$ such that $10 = n \times 20$ .

STEP 10

Attempt to find an integer $n$ that satisfies $10 = n \times 20$ .
Since $10 \div 20 = 0.5$ and 0.5 is not an integer, there is no integer $n$ that satisfies the equation.

STEP 11

Conclude that 10 is not a multiple of 20.

STEP 12

Check if 10 is a multiple of 25.
To be a multiple of 25, there must be an integer $n$ such that $10 = n \times 25$ .

STEP 13

Attempt to find an integer $n$ that satisfies $10 = n \times 25$ .
Since $10 \div 25 = 0.4$ and 0.4 is not an integer, there is no integer $n$ that satisfies the equation.

STEP 14

Conclude that 10 is not a multiple of 25.

STEP 15

Determine the true statement.
Based on the calculations, the only true statement is "10 is a multiple of 5."
The correct answer is: 10 is a multiple of 5.

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Which number is a multiple of 4, 5, and 20? 101010 is a multiple of 4, 5, and 20.

STEP 1

Assumptions1. We need to determine which of the given statements is true regarding the number 10 being a multiple of another number.

STEP 2

STEP 3

Check if 10 is a multiple of 4.To be a multiple of 4, there must be an integer n n n such that 10=n×4 10 = n \times 4 10=n×4.

STEP 4

Attempt to find an integer n n n that satisfies 10=n×4 10 = n \times 4 10=n×4.Since 10÷4=2.5 10 \div 4 = 2.5 10÷4=2.5 and 2.5 is not an integer, there is no integer n n n that satisfies the equation.

STEP 5

Conclude that 10 is not a multiple of 4.

STEP 6

Check if 10 is a multiple of 5.To be a multiple of 5, there must be an integer n n n such that 10=n×5 10 = n \times 5 10=n×5.

STEP 7

Attempt to find an integer n n n that satisfies 10=n×5 10 = n \times 5 10=n×5.Since 10÷5=2 10 \div 5 = 2 10÷5=2 and 2 is an integer, there is an integer n n n that satisfies the equation.

STEP 8

Conclude that 10 is a multiple of 5.

STEP 9

Check if 10 is a multiple of 20.To be a multiple of 20, there must be an integer n n n such that 10=n×20 10 = n \times 20 10=n×20.

STEP 10

Attempt to find an integer n n n that satisfies 10=n×20 10 = n \times 20 10=n×20.Since 10÷20=0.5 10 \div 20 = 0.5 10÷20=0.5 and 0.5 is not an integer, there is no integer n n n that satisfies the equation.

STEP 11

Conclude that 10 is not a multiple of 20.

STEP 12

Check if 10 is a multiple of 25.To be a multiple of 25, there must be an integer n n n such that 10=n×25 10 = n \times 25 10=n×25.

STEP 13

Attempt to find an integer n n n that satisfies 10=n×25 10 = n \times 25 10=n×25.Since 10÷25=0.4 10 \div 25 = 0.4 10÷25=0.4 and 0.4 is not an integer, there is no integer n n n that satisfies the equation.

STEP 14

Conclude that 10 is not a multiple of 25.

STEP 15

Determine the true statement.Based on the calculations, the only true statement is "10 is a multiple of 5."The correct answer is: 10 is a multiple of 5.

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Which number is a multiple of 4, 5, and 20? $10$ is a multiple of 4, 5, and 20.

Assumptions
1. We need to determine which of the given statements is true regarding the number 10 being a multiple of another number.

Check if 10 is a multiple of 4.
To be a multiple of 4, there must be an integer $n$ such that $10 = n \times 4$ .

Attempt to find an integer $n$ that satisfies $10 = n \times 4$ .
Since $10 \div 4 = 2.5$ and 2.5 is not an integer, there is no integer $n$ that satisfies the equation.

Check if 10 is a multiple of 5.
To be a multiple of 5, there must be an integer $n$ such that $10 = n \times 5$ .

Attempt to find an integer $n$ that satisfies $10 = n \times 5$ .
Since $10 \div 5 = 2$ and 2 is an integer, there is an integer $n$ that satisfies the equation.

Check if 10 is a multiple of 20.
To be a multiple of 20, there must be an integer $n$ such that $10 = n \times 20$ .

Attempt to find an integer $n$ that satisfies $10 = n \times 20$ .
Since $10 \div 20 = 0.5$ and 0.5 is not an integer, there is no integer $n$ that satisfies the equation.

Check if 10 is a multiple of 25.
To be a multiple of 25, there must be an integer $n$ such that $10 = n \times 25$ .

Attempt to find an integer $n$ that satisfies $10 = n \times 25$ .
Since $10 \div 25 = 0.4$ and 0.4 is not an integer, there is no integer $n$ that satisfies the equation.

Determine the true statement.
Based on the calculations, the only true statement is "10 is a multiple of 5."
The correct answer is: 10 is a multiple of 5.