Sara has $16$ red flowers and $28$ yellow flowers. She wants to make bouquets with the same number of each color flower in each Bouquet. What is the greatest number of bouquets she can make?

View step-by-step help

Home

Math Problems

Grade 7

GCF and LCM: word problems

Full solution

Q. Sara has

16

red flowers and

28

yellow flowers. She wants to make bouquets with the same number of each color flower in each Bouquet. What is the greatest number of bouquets she can make?

Identify Question: Identify what is being asked. $\newline$ We need to find the greatest number of bouquets Sara can make with an equal number of red and yellow flowers in each bouquet without any flowers left over.
Approach Determination: Determine the approach to solve the problem. $\newline$ To ensure each bouquet has the same number of red and yellow flowers with none left over, we need to find the greatest common factor (GCF) of the number of red and yellow flowers.
Red & Yellow Flowers: List the number of red and yellow flowers. $\newline$ Red flowers: $16$ $\newline$ Yellow flowers: $28$
Factors of Red Flowers: Find the factors of the number of red flowers. $\newline$ Factors of $16$ : $1$ , $2$ , $4$ , $8$ , $16$
Factors of Yellow Flowers: Find the factors of the number of yellow flowers. $\newline$ Factors of $28$ : $1$ , $2$ , $4$ , $7$ , $14$ , $28$
Common Factors Identification: Identify the common factors of $16$ and $28$ . $\newline$ Common factors: $1$ , $2$ , $4$
Greatest Common Factor Determination: Determine the greatest common factor (GCF). The GCF of $16$ and $28$ is $4$ .
Conclusion: Conclude the greatest number of bouquets Sara can make. $\newline$ Sara can make $4$ bouquets with an equal number of red and yellow flowers in each bouquet.