GCF Word Problems
Abbreviation for greatest common factor

Rebecca has 20 table tennis balls and 16 table tennis paddles. She wants to sell packages of balls and paddles bundled together. What is the greatest number of packages she can sell with no leftover balls or paddles?

There are 100 senators and 435 representatives in the United States Congress. How many identical groups could be formed from all the senators and representatives?

A choir director at your school wants to divide the choir into smaller groups. There are 24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each type of voice. A. What is the greatest number of groups that can be formed? B. How many sopranos altos and tenorn will be in each group? C. How many possible groups could be formed with equal numbers of each type of voice?

If Mary inspect every sixteenth calculator and Nancy inspects every thirtysixth calculator, which calculator will be the first that they both inspect?

Paul has three pieces of rope with lengths of 140 cm, 168 cm & 210 cm. He wishes to cut the three pieces of rope in to smaller pieces of equal length with no remainders. What is the greatest possible length of each of the smaller pieces of rope? How many of the smaller pieces of rope of equal length can he get altogether?

Find the greatest number which divides 6168, 2447 and 3118 leaving the same remainder in each case?

Bettina bought 75 pieces of cupcakes and 50 pieces of bottled water. What is the greatest amount of bottled water and cupcakes placed in each paper bag?

there was 33 cookies. the employes want to sell them to the eqyual amount of people. sandy had 10 cookies and bob hadt 23 more cookies. how many people can they give cookies to, to make a equal amount


The Math Club members are preparing identical welcome kits for the sixthgraders.They have 60 pencils and 48 memo pads.What is the greatest nymber of kits they can prepare using all of the pevcils and memo pads?


Jordan and manuel is on the trackandfield team at the school.running around the track one day,jordan ran 444 m and manuel ran 777 m.they both ran a whole numbers of times around the track.how far around is the track?

I have 300 strawberries and 60 bananas to make shakes. I want to use all of the fruit. How many equal whole bananas and whole straberries will I need to make the greatest number of shakes?


bob at a pie and forgot to do his homework?

there are 40 freshman, and 24 sophmores. They have to divide them into teams if there are same number of freshman and sophmores in each team how many teams ?


The greatest of two numbers is 850. neither number is divisible by the other. What is the smallest that these two numbers could be?



Brandon and carlos are members of the high school track team. They run different events; both events are multiple laps. At a recent track meets, carlos` 3rd place time for his event was 8 minutes and 32 seconds. Coincidentally, carlos` lap time was exactly twice as long as Brandon`s. Find their lap times  they both greater than 30 seconds. (Hint: convert time to second first)

Brandon and carlos are members of the high school track team. They run different events; both events are multiple laps. At a recent track meets, carlos\` 3rd place time for his event was 8 minutes and 32 seconds. Coincidentally, carlos\` lap time was exactly twice as long as Brandon\`s. Find their lap times  they both greater than 30 seconds. (Hint: convert time to second first)

a choir director in a certain school wants to divide the choir into smaller groups. there are 16 sopranos 40 altos and 24 tenors. each group will have the same number of each type of voice. what is the greatest number of groups that can be formed?

Elizabeth has three cd storage cases that can hold 16, 24, and 32 cds. The cases hae sections holding the same number of cds. What is the greatest number of cds in a section?

Vir, a custume designer has 36 bb, 27 pb, and 18 bcb she must use to create costumes. what is the largest number of costumes she can make without having aany buttons left over?

The Coverall Paint Company wants to sell paint in can sizes that most people would use up completely. The company has found out that most people paint wall surfaces of 300m2, 450m2, or 600m2. How many square metres of wall surface should the paint in their largest can cover?

7TH & 8TH GRADE CLASS IS PLANNING A DINNER. THERE ARE 168 STUDENTS IN THE 7TH GRADE & 112 STUDENTS IN THE 8TH GRADE. EACH GRADE SITS IN A DIFFERENT ROOM. HOW MANY CHAIRS ARE NEEDED IN EACH ROOM IF THE TOTAL NUMBER OF TABLES PER ROOM CANNOT EXCEED 15 AND THE TOTAL NUMBER OF CHAIRS PER TABLE CANNOT EXCEED 15. EACH TABLE IN EACH ROOM SHOLD HAVE THE SAME NUMBER OF CHAIRS

sides of square are lengthened by 8cm, the area becomes 256cm^2. Find the length of a side of the original square

a choir director at your school wants to divide the choir into smaller groups. there are 24 sopranos, 60 altos,and 36 tenors. each group will have the same number of each type of voice. what is the greatest number of groups that can be formed?

the largest factor that numbers share


16 boys and 12 girls. Greatest number of teams possible with the same number of boys and girls on each team. How many teams were made up if each person was on a team? How many girls on each team? How many boys on each team?