Divisibility and Number Properties

This video tutorial explores a mathematical trick involving the number 73. It guides viewers through a series of steps using a calculator to demonstrate that any four-digit number entered twice is divisible by 137 and the original number, ultimately resulting in 73. The video explains the underlying mathematical principle, showing that the eight-digit number is the product of the original number, 73, and 137. This is due to the fact that 10,001 equals 73 times 137, which simplifies the calculation to always yield 73.

What is the first step in the activity described in the video?

• Divide a number by 137.

• Enter a four-digit number into a calculator.

• Multiply a number by 10,001.

• Write the number 73 on a piece of paper.

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CCSS.3.OA.D.9

What should you do after entering a four-digit number twice into the calculator?

• Announce the number is divisible by 137.

• Announce the number is divisible by 73.

• Multiply the number by 10,001.

• Write the number on a piece of paper.

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CCSS.5.NBT.B.6

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What is the result when the eight-digit number is divided by 137?

• A decimal number

• A whole number

• The original four-digit number

• The number 73

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CCSS.5.NBT.B.6

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After dividing by 137, what is the next step in the process?

• Announce the number is divisible by 73

• Multiply by 10,001

• Write the result on paper

• Divide by the original four-digit number

Why does the process always result in the number 73?

• Because 73 is a prime number

• Because the calculator is programmed to do so

• Because the original number is always 73

• Because 10,001 equals 73 times 137

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CCSS.5.NBT.A.2

What is the mathematical expression for a four-digit number entered twice?

• The four-digit number times 73

• The four-digit number times 137

• The four-digit number times 100

• The four-digit number times 10,001

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CCSS.5.NBT.A.2

What is the significance of the number 10,001 in the process?

• It is the original four-digit number

• It is the product of 73 and 137

• It is the sum of 73 and 137

• It is a random number

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CCSS.5.NBT.B.6

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What happens when you divide the product by the original four-digit number?

• You get the number 73

• You get a decimal number

• You get the original number

• You get the number 137

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CCSS.5.NBT.B.6

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Why does dividing by the original four-digit number simplify the process?

• Because it subtracts from the original number

• Because it cancels out the original number

• Because it adds to the original number

• Because it multiplies the original number

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CCSS.5.NBT.A.2

What is the final result of the entire process?

• The original four-digit number

• The number 137

• The number 73

• The number 10,001

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CCSS.5.NBT.A.2