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At a family reunion, a family friend brings 20 pounds of ice and 30 cups. Which expression shows the greatest common factor, using the Distributive Property, of 20 and 30 ?

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The expression for the greatest common factor of 20 and 30 using the distributive property is 10(2 + 3)

Pounds of ice = 20

Number of cups = 30

The relation for the distributive property :

a × (b + c)

Expand ;

a × (b + c) = (a × b) + (a × c) = ab + ac

Finding the greatest common factor of 20 and 30 ;

  • 20 = 2 × 10

  • 30 = 3 × 10

(2 × 10) + (3 × 10)

According to the distributive property

(2 × 10) + (3 × 10) = 10(2 + 3)

Therefore, the expression for the greatest common factor is 10(2 + 3)

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