nisha is putting 64 cookies and 40 truffles into gift boxes. Each box willhave the same number of cookies and chocolate truffles. What is the reatest number of boxes Nisha can make with no cookies or chocolate truffles left over?
I guessed 8 because it goes into 64 and 40 - but I don't know how and need to show work for this. Is it right anyway?
The greatest common factor of 64 and 40 is 8.
http://www.mathsisfun.com/greatest-common-factor.html
To find the greatest number of boxes Nisha can make with no cookies or truffles left over, we need to determine the highest common factor (HCF) of 64 and 40.
To find the HCF, we can use the prime factorization method as follows:
Step 1: Prime factorization of 64:
64 = 2 * 32 = 2 * 2 * 16 = 2² * 2 * 8 = 2² * 2 * 2 * 4 = 2² * 2 * 2 * 2² = 2⁶
Step 2: Prime factorization of 40:
40 = 2 * 20 = 2 * 2 * 10 = 2 * 2 * 2 * 5 = 2³ * 5
Step 3: Determine the common factors:
Comparing the prime factorization of 64 and 40, we see that they have a common factor of 2 to the power of 3 (2³).
Step 4: Calculate the HCF:
The highest common factor (HCF) is obtained by multiplying the common factors together:
HCF = 2³ = 8
Therefore, the greatest number of boxes Nisha can make with no cookies or truffles left over is 8. Your guess was correct!
To find the greatest number of boxes Nisha can make with no cookies or truffles left over, we need to find the highest common factor of 64 and 40.
The first step is to find the prime factorization of both numbers:
Prime factorization of 64:
64 = 2 * 2 * 2 * 2 * 2 * 2 = 2^6
Prime factorization of 40:
40 = 2 * 2 * 2 * 5 = 2^3 * 5
Next, we find the common factors of both numbers by taking the lowest exponent for each prime factor:
Common factors:
2^3 = 2 * 2 * 2 = 8
So the greatest number of boxes Nisha can make with no cookies or truffles left over is 8. Your guess was correct!