# Worksheet: The Greatest Common Factor

Q1:

Find the greatest common factor of 26 and 14.

Q2:

Find the greatest common factor of 63 and 42.

Q3:

Find the greatest common factor of 9 and 14.

Q4:

Find the greatest common factor of 7,15, and 21.

Q5:

By taking out the greatest common factor (GCF), find the value of , without using a calculator.

• A 28
• B
• C 988
• D
• E

Q6:

Find the greatest common factor of 110, 40, and 120.

Q7:

Find the GCF of 63, 90, and 30.

• A 5
• B 7
• C 21
• D 3
• E 4

Q8:

Which of the following sets of numbers has an GCF that is equal to one of its numbers?

• A
• B
• C
• D
• E

Q9:

Find the GCF of 84 and 28.

• A 7
• B 3
• C 21
• D 28
• E 4

Q10:

Find the GCF for 16 gallons, 24 gallons, 36 gallons, and 50 gallons.

Q11:

Find the greatest common factor of 21 and 10.

Q12:

A movie club hosted a movie night for students. Given that each student paid the same amount to attend, determine the highest possible cost per student for the movie night, and find how many students attended.

 Arrival Time Money Collected 5:00 pm to 6:00 pm 6:00 pm to 7:00 pm 7:00 pm to 8:00 pm 8:00 pm to 9:00 pm \$44 \$30 \$34 \$26
• A\$4, 67
• B\$2, 134
• C\$1, 33
• D\$2, 67
• E\$4, 134

Q13:

The table shows the amounts of money that were raised for charity by selling various items in three different events. If all items were of the same price and under \$10, find the maximum possible item’s price, and then determine how many items were sold in each event.

 Show Sales Event A Event B Event C \$1 345 \$1 135 \$1 950
• Aitem price: \$5, Event A: 269 items, Event B: 227 items, Event C: 395 items
• Bitem price: \$6, Event A: 269 items, Event B: 227 items, Event C: 390 items
• Citem price: \$6, Event A: 269 items, Event B: 227 items, Event C: 395 items
• Ditem price: \$5, Event A: 269 items, Event B: 227 items, Event C: 390 items
• Eitem price: \$5, Event A: 269 items, Event B: 236 items, Event C: 395 items

Q14:

Which of the following choices represents three numbers whose greatest common factor is 17?

• A357, 306, 204
• B119, 238, 357
• C238, 204, 136
• D119, 102, 68
• E102, 204, 510

Q15:

William has a collection of colored seashells that he keeps in bags. The number of shells of each color in his collection is summarized in the table. All of the bags contain an equal number of shells, and each one contains shells of only one color. If the number of shells in each bag is as large as it can be, given the other conditions, determine the number of bags required for each color.

 Color Number Red Blue Yellow 168 56 140
• ARed seashells: 6 bags, blue seashells: 3 bags, yellow seashells: 6 bags
• BRed seashells: 6 bags, blue seashells: 2 bags, yellow seashells: 6 bags
• CRed seashells: 7 bags, blue seashells: 3 bags, yellow seashells: 6 bags
• DRed seashells: 6 bags, blue seashells: 2 bags, yellow seashells: 5 bags
• ERed seashells: 7 bags, blue seashells: 2 bags, yellow seashells: 5 bags