The Greatest Common **Factor** (GCF) is a fundamental concept in number theory. It’s the largest number that divides evenly into two (or more) integers. Understanding the concept of GCF is important for various mathematical operations, including simplifying fractions, working with least common multiples, and understanding divisibility rules.This article includes 50+ greatest common factor questions.

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## Why is the (Greatest Common Factor) GCF Important?

The GCF has numerous applications in mathematics, especially when dealing with fractions. It helps simplify fractions by finding the greatest common factor between the numerator and denominator. Additionally, the GCF plays a role in concepts like least common multiple (LCM), which is the smallest number that is a multiple of all the given numbers.

## Methods to Follow to Find the Greatest Common Factor

There are several ways to find the GCF, each with its own advantages depending on the complexity of the numbers involved. Here are the three most common methods:

- Factoring
**:**This method involves listing out all the factors of each number and then identifying the largest factor that’s common to all of them. It’s a good choice for small sets of numbers. - Prime Factorization: This method breaks down each number into its prime factors (numbers divisible only by 1 and itself). The GCF is then found by multiplying the common prime factors raised to the highest power that appears in any of the numbers. This method becomes more efficient as the numbers get larger.
- Euclid’s Algorithm: This is a more advanced method that involves a step-by-step subtraction process to find the GCF. It’s particularly useful for very large numbers.

## Tips to Solve Greatest Common Factor Questions

Remember, practice is key! Here are some additional tips to strengthen your GCF skills:

- As you solve more problems, you’ll start noticing patterns in divisibility rules that can help you identify the GCF quickly.
- Don’t just list out all the factors. See if you can find a more efficient way to arrive at the GCF, especially for larger numbers.
- There are many interactive platforms and tutorials available online that can provide additional practice and explanations.

## 50+ Questions on Greatest Common Factor Questions

What is the GCF of 24 and 36?

A) 4

B) 6

C) 12

D) 24

Answer: C) 12

Which of the following is a factor of both 18 and 24?

A) 5

B) 6

C) 7

D) 8

Answer: B) 6

What is the GCF of 45 and 63?

A) 3

B) 9

C) 15

D) 21

Answer: A) 3

If the GCF of two numbers is 8 and one of the numbers is 32, what could be the other number?

A) 12

B) 24

C) 48

D) 64

Answer: B) 24

The GCF of two prime numbers is always:

A) 1

B) 2

C) 3

D) The numbers themselves

Answer: A) 1

What is the GCF of 16 and 24?

A) 4

B) 6

C) 8

D) 12

Answer: C) 8

If the GCF of two numbers is 15 and one of the numbers is 45, what could be the other number?

A) 30

B) 75

C) 60

D) 90

Answer: B) 75

What is the GCF of 36 and 48?

A) 6

B) 8

C) 12

D) 24

Answer: C) 12

If the GCF of two numbers is 1, then the numbers are:

A) Prime to each other

B) Not prime to each other

C) Both prime

D) None of the above

Answer: A) Prime to each other

What is the GCF of 20 and 25?

A) 2

B) 5

C) 10

D) 15

Answer: B) 5

If the GCF of two numbers is 20 and one of the numbers is 100, what could be the other number?

A) 80

B) 120

C) 200

D) 300

Answer: A) 80

What is the GCF of 27 and 36?

A) 3

B) 6

C) 9

D) 12

Answer: C) 9

The GCF of two numbers is always less than or equal to:

A) The sum of the numbers

B) The difference of the numbers

C) The product of the numbers

D) The quotient of the numbers

Answer: A) The sum of the numbers

If the GCF of two numbers is 12 and one of the numbers is 36, what could be the other number?

A) 48

B) 60

C) 72

D) 84

Answer: B) 60

What is the GCF of 72 and 108?

A) 6

B) 12

C) 18

D) 36

Answer: B) 12

If the GCF of two numbers is 9 and one of the numbers is 63, what could be the other number?

A) 72

B) 81

C) 90

D) 99

Answer: B) 81

What is the GCF of 54 and 90?

A) 6

B) 9

C) 18

D) 27

Answer: B) 9

If the GCF of two numbers is 15 and one of the numbers is 75, what could be the other number?

A) 45

B) 60

C) 90

D) 105

Answer: C) 90

What is the GCF of 80 and 120?

A) 10

B) 20

C) 40

D) 60

Answer: B) 20

If the GCF of two numbers is 25 and one of the numbers is 75, what could be the other number?

A) 100

B) 125

C) 150

D) 175

Answer: A) 100

What is the GCF of 54 and 72?

A) 6

B) 9

C) 18

D) 27

Answer: B) 9

If the GCF of two numbers is 16 and one of the numbers is 64, what could be the other number?

A) 80

B) 96

C) 112

D) 128

Answer: B) 96

What is the GCF of 63 and 81?

A) 3

B) 9

C) 18

D) 27

Answer: B) 9

If the GCF of two numbers is 25 and one of the numbers is 100, what could be the other number?

A) 125

B) 150

C) 175

D) 200

Answer: B) 150

What is the GCF of 36 and 54?

A) 6

B) 9

C) 12

D) 18

Answer: C) 18

If the GCF of two numbers is 14 and one of the numbers is 56, what could be the other number?

A) 70

B) 84

C) 98

D) 112

Answer: B) 84

What is the GCF of 45 and 75?

A) 5

B) 15

C) 25

D) 35

Answer: B) 15

If the GCF of two numbers is 36 and one of the numbers is 72, what could be the other number?

A) 108

B) 144

C) 180

D) 216

Answer: A) 108

What is the GCF of 80 and 100?

A) 10

B) 20

C) 30

D) 40

Answer: B) 20

If the GCF of two numbers is 7 and one of the numbers is 49, what could be the other number?

A) 63

B) 77

C) 91

D) 105

Answer: A) 63

What is the GCF of 42 and 63?

A) 7

B) 14

C) 21

D) 28

Answer: C) 21

If the GCF of two numbers is 32 and one of the numbers is 96, what could be the other number?

A) 128

B) 160

C) 192

D) 224

Answer: C) 192

What is the GCF of 72 and 90?

A) 6

B) 9

C) 18

D) 36

Answer: B) 9

If the GCF of two numbers is 18 and one of the numbers is 54, what could be the other number?

A) 72

B) 90

C) 108

D) 126

Answer: B) 90

What is the GCF of 60 and 84? A) 6 B) 12 C) 18 D) 24 Answer: B) 12

If the GCF of two numbers is 21 and one of the numbers is 63, what could be the other number?

A) 84

B) 105

C) 126

D) 147

Answer: A) 84

What is the GCF of 48 and 72? A) 6 B) 12 C) 16 D) 24 Answer: B) 12

If the GCF of two numbers is 28 and one of the numbers is 84, what could be the other number?

A) 112

B) 140

C) 168

D) 196

Answer: C) 168

What is the GCF of 56 and 84?

A) 4

B) 8

C) 12

D) 28

Answer: D) 28

If the GCF of two numbers is 15 and one of the numbers is 45, what could be the other number?

A) 60

B) 75

C) 90

D) 105

Answer: B) 75

What is the GCF of 63 and 105?

A) 7

B) 21

C) 35

D) 42

Answer: B) 21

If the GCF of two numbers is 20 and one of the numbers is 100, what could be the other number?

A) 120

B) 140

C) 160

D) 180

Answer: A) 120

What is the GCF of 84 and 126?

A) 6

B) 14

C) 21

D) 42

Answer: C) 21

If the GCF of two numbers is 30 and one of the numbers is 90, what could be the other number?

A) 120

B) 150

C) 180

D) 210

Answer: B) 150

What is the GCF of 75 and 125?

A) 5

B) 15

C) 25

D) 35

Answer: C) 25

If the GCF of two numbers is 48 and one of the numbers is 144, what could be the other number?

A) 192

B) 240

C) 288

D) 336

Answer: A) 192

What is the GCF of 99 and 132?

A) 3

B) 11

C) 33

D) 44

Answer: A) 3

If the GCF of two numbers is 36 and one of the numbers is 108, what could be the other number?

A) 144

B) 180

C) 216

D) 252

Answer: A) 144

What is the GCF of 80 and 160?

A) 10

B) 20

C) 40

D) 80

Answer: B) 20

If the GCF of two numbers is 42 and one of the numbers is 126, what could be the other number?

A) 168

B) 210

C) 252

D) 294

Answer: A) 168

What is the GCF of 88 and 132?

A) 4

B) 8

C) 22

D) 44

Answer: C) 22

If the GCF of two numbers is 50 and one of the numbers is 150, what could be the other number?

A) 200

B) 250

C) 300

D) 350

Answer: A) 200

What is the GCF of 72 and 144?

A) 6

B) 12

C) 18

D) 36

Answer: B) 12

If the GCF of two numbers is 16 and one of the numbers is 128, what could be the other number?

A) 144

B) 160

C) 176

D) 192

Answer: A) 144

What is the GCF of 90 and 135?

A) 5

B) 9

C) 15

D) 27

Answer: B) 9

If the GCF of two numbers is 28 and one of the numbers is 84, what could be the other number?

A) 112

B) 140

C) 168

D) 196

Answer: C) 168

What is the GCF of 81 and 108?

A) 9

B) 12

C) 18

D) 27

Answer: A) 9

If the GCF of two numbers is 18 and one of the numbers is 54, what could be the other number?

A) 72

B) 90

C) 108

D) 126

Answer: B) 90

What is the GCF of 120 and 180?

A) 20

B) 30

C) 40

D) 60

Answer: D) 60

If the GCF of two numbers is 15 and one of the numbers is 45, what could be the other number?

A) 60

B) 75

C) 90

D) 105

Answer: B) 75

**Related Blogs**

## FAQs

**What is the GCF of 18 and 24?**

GCF of 18 and 24 is 6.

**What is the GCF of 24 and 36?**

GCF of 24 and 36 is 12.

**What is the GCF of 24 and 30?**

GCF of 24 and 30 is 6.

**What is the GCF of 28 and 32?**

GCF of 28 and 32 is 4.

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