Mei has 15 oranges, and 9 peaches. She wants to put all of the fruit into decorative baskets. Each basket must have the same number of pieces of fruit in it. What is the greatest number of fruit Mei can put in each basket? Explain.
the GCF (greatest common factor) of 15 and 9 is 3
so 5 oranges and 3 peaches in each of 3 baskets
To find the greatest number of fruit Mei can put in each basket, we need to find the greatest common divisor (GCD) of 15 and 9. The GCD represents the largest positive integer that divides both numbers without leaving a remainder.
To find the GCD, we can use the Euclidean algorithm:
Step 1: Divide 15 by 9: 15 ÷ 9 = 1, remainder 6
Step 2: Divide 9 by 6: 9 ÷ 6 = 1, remainder 3
Step 3: Divide 6 by 3: 6 ÷ 3 = 2, remainder 0
Once we reach a remainder of 0, we can stop.
The GCD of 15 and 9 is the last non-zero remainder, which is 3.
Therefore, Mei can put 3 pieces of fruit in each basket, ensuring all baskets have the same number of fruit.