you are making identical gift bags using 24 candles and 36 bottles of lotion. What is the greatest number of gift bags you can make with no items left over.
What is the greatest common factor of 24 and 36?
17 bags
To find the greatest number of gift bags you can make with no items left over, we need to find the highest common factor or greatest common divisor (GCD) of the number of candles and bottles of lotion.
Step 1: Determine the prime factors of both numbers.
The prime factors of 24 are 2^3 * 3, which can be written as 2 * 2 * 2 * 3.
The prime factors of 36 are 2^2 * 3^2, which can be written as 2 * 2 * 3 * 3.
Step 2: Identify the common prime factors.
The common prime factors between 24 and 36 are 2 and 3.
Step 3: Find the highest exponent for each common prime factor.
The highest exponent of 2 is 2 (found in both 24 and 36).
The highest exponent of 3 is 1 (found in 24 but not in 36).
Step 4: Multiply the common prime factors with the highest exponent.
Multiply 2^2 * 3^1 = 4 * 3 = 12.
Therefore, you can make a maximum of 12 gift bags with no items left over using 24 candles and 36 bottles of lotion.