Questions: Greatest Common Factor (GCF) - Quiz - Level F Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? What is the greatest number of packages of soap and toothbrushes that Marcus can make? Marcus can make at most packages.

Greatest Common Factor (GCF) - Quiz - Level F Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? What is the greatest number of packages of soap and toothbrushes that Marcus can make? Marcus can make at most packages.
Transcript text: Greatest Common Factor (GCF) - Quiz - Level F Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? What is the greatest number of packages of soap and toothbrushes that Marcus can make? Marcus can make at most $\square$ packages.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the quantities

Marcus has 36 bars of soap and 24 toothbrushes.

Step 2: Find the GCF of 36 and 24

To determine the greatest number of identical packages, we need to find the greatest common factor (GCF) of 36 and 24.

  • The factors of 36 are: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \).
  • The factors of 24 are: \( 1, 2, 3, 4, 6, 8, 12, 24 \).
Step 3: Determine the GCF

The greatest common factor of 36 and 24 is \( 12 \).

Step 4: Calculate the number of packages

Marcus can make at most \( 12 \) identical packages using all the soap and toothbrushes.

Final Answer

Marcus can make at most \( \boxed{12} \) packages.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Solve the following system of equations with the substitution method: x-4y=21 3x-5y=35 Answer: (x, y)= Preview x : Preview y : Enter your answers as integers or as reduced fractions in the form A/B.
failedAnswered
Find the slope and the y intercept of the graph of the linear equation. Write your answers in simplest form. 0=4.5-2 y+4.8 x
failedAnswered
Evaluate each expression. (a) log base 7 of 1 = (b) log base 9 of 1/81 =
failedAnswered
The complement of a 51° angle is 39°
failedAnswered
-4x + y = 12 -8x + 2y = 24 Graph the linear equations by writing the equations in slope-intercept form: y = x + y = x + Identify the appropriate number of solutions. If there is a solution, give the point: One Solution ( , )