A baker has 12 chocolate cupcakes and 15 vanilla cupcakes. She wants to package them into … — ACT

A baker has $12$ chocolate cupcakes and $15$ vanilla cupcakes. She wants to package them into boxes such that each box has the same number of chocolate cupcakes and the same number of vanilla cupcakes, with no cupcakes left over. What is the greatest number of boxes she can make?

$3$ Answer
B
$5$
C
$27$
D
$60$
E
$180$

Answer

The greatest number of boxes she can make is

3

The greatest number of boxes that can be made is found by calculating the greatest common factor (GCF) of the two cupcake quantities. The factors of

12

are

1, 2, 3, 4, 6,

and

12

. The factors of

15

are

1, 3, 5,

and

15

. The greatest factor common to both lists is

3

. This allows the baker to make

3

boxes, each containing

4

chocolate cupcakes and

5

vanilla cupcakes.

Step-by-Step Solution

Identify that the problem requires finding the greatest common factor (GCF) of

12

and

15

to distribute the cupcakes evenly into the maximum number of boxes.

The problem is recognized as a greatest common factor (GCF) calculation.

We need the largest integer that divides both

12

and

15

with no remainder.

List the factors of

12

and

15

Factors of

12

are

1, 2, 3, 4, 6, 12

. Factors of

15

are

1, 3, 5, 15

Listing the factors helps identify all shared divisors.

Find the greatest common factor shared by both lists.

The common factors are

1

and

3

, so the greatest common factor is

3

The greatest common factor is the largest number of identical groups we can form.

Key Concept

Factors, Multiples, and Prime Factorization

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic