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Lesson: The Greatest Common Factor

In this lesson, we will learn how to find the greatest common factor of two or more numbers by writing all the factors of those numbers.

Video

08:58

Sample Question Videos

02:29
02:12

Worksheet • 19 Questions • 2 Videos

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 highest common factor (HCF), find the value of 2 × 5 − 2 6 × 2 − 1 7 × 2 , without using a calculator.

Q6:

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

Q7:

Find the HCF of 63, 90, and 30.

Q8:

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

  • A 3 , 3 9 , 3 0
  • B 4 0 , 2 0 , 2 9
  • C 2 , 2 5 , 2 1
  • D 4 4 , 3 7 , 2
  • E 1 9 , 3 4 , 4 6

Q9:

Find the HCF of 84 and 28.

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 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
Money Collected $44 $30 $34 $26
  • A$2, 67
  • B$4, 134
  • C$2, 134
  • D$1, 33
  • E$4, 67

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

Q14:

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

  • A119, 102, 68
  • B102, 204, 510
  • C119, 238, 357
  • D238, 204, 136
  • E357, 306, 204

Q15:

Nabil has a collection of coloured seashells that he keeps in bags. The number of each coloured shell in his collection is summarised in the table. All of the bags contain an equal number of shells, and each one contains shells of only one colour. 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 colour.

Colour Red Blue Yellow
Number 168 56 140
  • Ared seashells: 6 bags, blue seashells: 2 bags, yellow seashells: 5 bags
  • Bred seashells: 7 bags, blue seashells: 2 bags, yellow seashells: 5 bags
  • Cred seashells: 6 bags, blue seashells: 2 bags, yellow seashells: 6 bags
  • Dred seashells: 7 bags, blue seashells: 3 bags, yellow seashells: 6 bags
  • Ered seashells: 6 bags, blue seashells: 3 bags, yellow seashells: 6 bags

Q16:

Find the greatest common factor of 175 and 25.

Q17:

Mr. Fady is organizing his vinyl collection into boxes by genre. Given that he wants to put the same number of vinyls in each of the boxes without mixing genres, determine the largest number of vinyls he can put into one box and the number of boxes needed.

Genre Rock Pop Jazz
Number of Vinyls 70 95 100
  • A5 vinyls, 53 boxes
  • B6 vinyls, 54 boxes
  • C5 vinyls, 54 boxes
  • D15 vinyls, 54 boxes
  • E15 vinyls, 53 boxes

Q18:

Determine the GCF of all the numbers in the following list: 7 , 1 4 , 2 1 , 2 8 , … .

Q19:

If 𝑓 ∶ ℝ → ℝ + , where 𝑓 ( 𝑥 ) = 𝑥 − 2 0 , and 𝑔 ∶ [ − 9 , 2 1 ] → ℝ , where 𝑔 ( 𝑥 ) = 𝑥 − 4 , determine 𝑓 𝑔 ( 𝑥 ) and its domain.

  • A 𝑓 𝑔 ( 𝑥 ) = 𝑥 − 2 0 𝑥 − 4 , 𝑥 ∈ ] 0 , 2 1 ] − { 4 }
  • B 𝑓 𝑔 ( 𝑥 ) = 𝑥 − 4 𝑥 − 2 0 , 𝑥 ∈ ] 0 , 2 1 ] − { 4 }
  • C 𝑓 𝑔 ( 𝑥 ) = 𝑥 − 4 𝑥 − 2 0 , 𝑥 ∈ ] 0 , 2 1 ] − { 2 0 }
  • D 𝑓 𝑔 ( 𝑥 ) = 𝑥 − 2 0 𝑥 − 4 , 𝑥 ∈ ] 0 , 2 1 ] − { 2 0 }
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