Question

A party planner is making gift bags for an event. He has 96 pencils,

Answer 1

Considering the greatest common divisor, you obtain:

• the greatest number of gift bags that the party planner can make is 12.
• the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

Greatest common divisor

The greatest common divisor is the largest number that exactly divides two or more numbers at the same time. That is, it is the largest number by which two or more numbers can be divided, resulting in a whole number.

A method to calculate the greatest common factor must follow the following steps:

• Decompose or separate each number into prime factors.
• Common factors are noted.
• In each of the commons, the factor with the smallest exponent is chosen.
• Multiply the chosen factors.

This case

To find the greatest number of gift bags the party planner can make, you find the greatest common divisor.

To do this, decompose the numbers 96, 36 and 24:

• 96= 2⁵×3
• 36= 2²×3²
• 24= 2³×3

The common factors with the smallest exponent are: 2² and 3

So, the greatest common divisor between 96, 26 and 24 is calculated as: 2²×3= 4×3= 12

This means that the greatest number of gift bags that the party planner can make is 12.

To calculate the number of each item present in each bag, you divide the quantity of each item by the quantity of gift bags:

• 96 pencils÷ 12= 8 pencils
• 36 erasers÷ 12= 3 erasers
• 24 pencil toppers÷ 12= 2 pencil toppers

Finally, the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

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