Factors, Multiples and Divisibility Rules
  • 1. Peter's Party Zone sells cups in packages of 6 66 and plates in packages of 8 88. Shaniya is hosting a birthday party for her little sister and wants to have the same number of each item. What is the least number of packages of plates Shaniya needs to buy?
A) 5
B) 4
C) 3
D) 6
  • 2. Enzo and Beatriz are playing games at their local arcade. Incredibly, Enzo wins 5 55 tickets from every game, and Beatriz wins 11 1111 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. What is the minimum number of games that Enzo could have played?
A) 15
B) 22
C) 11
D) 33
  • 3. Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He has 72 7272 pencils and 24 2424 calculators and he must use all of the pencils and calculators. If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?
A) 3
B) 6
C) 12
D) 9
  • 4. Sherman goes golfing every 6 th 6 th 6, start superscript, start text, t, h, end text, end superscript day and Brad goes golfing every 7 th 7 th 7, start superscript, start text, t, h, end text, end superscript day. If Sherman and Brad both went golfing today, how many days until they will go golfing on the same day again?
A) 35
B) 36
C) 49
D) 42
  • 5. Abe is going to plant 54 5454 oak trees and 27 2727 pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
A) 29
B) 27
C) 28
D) 30
  • 6. Camryn practices the trumpet every 1 1 th 11 th 11, start superscript, start text, t, h, end text, end superscript day and the flute every 3 rd 3 rd 3, start superscript, start text, r, d, end text, end superscript day. Camryn practiced both the trumpet and the flute today. How many days until Camryn practices the trumpet and flute again in the same day?
A) 31
B) 39
C) 36
D) 33
  • 7. Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 8686 chocolate chip cookies and 42 4242 sugar cookies. Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies. What is the greatest number of identical packages that Shaquira can make?
A) 6
B) 2
C) 4
D) 0
  • 8. At the gym, Hillary swims every 6 days, runs every 4 days and cycles every 16 days. If she did all three activities today, in how many days will she do all three activities again on the same day?
A) 44
B) 42
C) 46
D) 48
  • 9. Oscar needs to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs. He can pack only one type of CD in each box and he must pack the same number of CDs in each box. What is the greatest number of CDs Oscar can pack in each box?
A) 5
B) 2
C) 4
D) 3
  • 10. I want to plant 45 sunflower plants, 81 corn plants and 63 tomato plants in my garden. If I put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants I can put in one row?
A) 8
B) 11
C) 10
D) 9
  • 11. Cups are sold 6 to a package and plates are sold 8 to a package. If you want to have the same number of each item for a party, what is the least number of packages of each you need to buy?
A) 4 and 3
B) 8 and 7
C) 6 and 5
D) 2 and 1
  • 12. A full moon occurs every 30 days. If the last full moon occurred on a Friday, how many days will pass before a full moon occurs again on a Friday?
A) 210
B) 215
C) 220
D) 205
  • 13. A cookie factory made 2,560 oatmeal cookies. After arranging the cookies into packages, the factory did not have any cookies left over. How many cookies could have gone in each package?
A) 3
B) 10
C) 6
D) 9
  • 14. 5,684 students voted in the student council election. Each candidate got the exact same number of votes. How many candidates could there have been?
A) 5
B) 9
C) 2
D) 3
  • 15. 748 people voted in the Westford City Council election. Each candidate received the exact same number of votes. How many city council candidates could there have been?
A) 9
B) 5
C) 6
D) 4
  • 16. There are 159 olives in the jars in the pantry. If each jar contains the exact same number of olives, how many jars could there be?
A) 2
B) 3
C) 9
D) 10
  • 17. The students at Mary's school need to form teams for field day. Each team must have the same number of students, and every student at the school must be on a team. If there are 368 students at Mary's school, how many teams could the students form?
A) 4
B) 5
C) 10
D) 9
  • 18. There are 7,299 students living in the dorms at a university. The same number of students live in each dorm. How many dorms could there be at the university?
A) 5
B) 10
C) 9
D) 6
  • 19. Martha wants to arrange 670 roses into vases. How many roses could she put in each vase without having any leftover roses?
A) 10
B) 4
C) 3
D) 6
  • 20. A farmer picked 48 peaches. She needs to divide the peaches into baskets to sell at the market. The farmer wants to put the same number of peaches in each bag with no peaches left over. How many peaches could the farmer put in each bag?
A) 9
B) 4
C) 5
D) 10
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