A football coach divides 42 players and 12 coaches into groups. Each group will have the same number of players and coaches. What is the greatest number of groups that can be formed.
Answer: 6 groups
Then it states use the greatest common factor 6 from the answer above to rewrite using the distributive property.
What numbers would I use to do the distributive property?
Would it be 6(42 + 12)?
6(7 + 2)
Since 6×7=42 and 6×2=12
To find the greatest number of groups that can be formed with equal number of players and coaches, we need to find the greatest common divisor (GCD) of both 42 and 12. The GCD represents the largest number that divides both of these numbers evenly.
To find the GCD of 42 and 12, we can use the Euclidean algorithm.
Step 1: Divide 42 by 12: The quotient is 3 and the remainder is 6.
Step 2: Divide 12 by 6: The quotient is 2 and the remainder is 0.
Since the remainder is 0, we know that 6 is a divisor of both 42 and 12. Thus, the greatest common divisor of 42 and 12 is 6.
Therefore, the greatest number of groups that can be formed with equal number of players and coaches is 6.
Why would you not just ad 42 + 12=54
6(54)
42 times 6=252
12 times 6=72
252+72=324
54x6=324
Why would you not do it like I did above?