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Lesson 3: Greatest Common Factor (GCF) and Applications — Practice Questions

  1. 1. A grocer wants to make identical fruit baskets using 30 apples and 45 oranges. What is the greatest number of identical baskets he can make with no fruit left over? ___

  2. 2. A host is creating identical party favor bags with 56 stickers and 24 lollipops. What will each bag contain if they make the maximum number of bags possible?

    • A. 7 stickers and 3 lollipops
    • B. 8 stickers and 3 lollipops
    • C. 14 stickers and 6 lollipops
    • D. 4 stickers and 2 lollipops

  3. 3. A club advisor is making identical supply kits using 40 notebooks and 32 markers. If each kit has 5 notebooks, how many markers will each kit have? ___

  4. 4. When dividing 20 red marbles and 25 blue marbles into the largest possible number of identical groups, what does the GCF of 20 and 25 represent?

    • A. The total number of marbles in each group
    • B. The maximum number of identical groups
    • C. The number of red marbles in each group
    • D. The total number of marbles

  5. 5. A florist is arranging bouquets with 18 daisies, 27 tulips, and 36 lilies. What is the greatest number of identical bouquets she can create with no flowers left over? ___

  6. 6. What is the greatest common factor (GCF) of 45 and 60? The GCF is ___.

  7. 7. The prime factorization of 56 is $2^3 \cdot 7$ and 98 is $2 \cdot 7^2$. What is the GCF of 56 and 98?

    • A. $2 \cdot 7$
    • B. $2^3 \cdot 7^2$
    • C. $2 \cdot 7^2$
    • D. $2^3 \cdot 7$

  8. 8. Using prime factorization, find the greatest common factor (GCF) of 70 and 98. The GCF is ___.

  9. 9. Which statement best defines the greatest common factor (GCF) of two numbers?

    • A. The smallest number that is a multiple of both numbers.
    • B. The largest number that divides evenly into both numbers.
    • C. The product of all the prime factors from both numbers.
    • D. The smallest prime factor shared by both numbers.

  10. 10. The sum $36 + 54$ can be simplified using the GCF. This can be rewritten as a product in the form $\_\_\_(2+3)$.