Question

A gardener has 1826 red flowers and 2486 yellow flowers. He wants to arrange them into the largest possible equal groups such that each group has the same number of red and yellow flowers. What is the maximum number of flowers in each group?

• A. 11
• B. 22
• C. 33
• D. 10

Answer 1

Answer:

B. 22

The maximum number of flowers in each group is 22.

To solve this problem, you need to find the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of the two quantities, 1826 and 2486.

Prime Factorization

Breaking down both numbers into their prime components:

• Prime factorization of 1826: $2 \times 11 \times 83$

• Prime factorization of 2486: $2 \times 11 \times 113$

Identify the Common Factors:

• Both numbers share the prime factors 2 and 11.

• $\text{HCF} = 2 \times 11 = 22$

Therefore, the largest equal group size possible that perfectly divides both sets of flowers without any remainders is 22.