GCF of 22 and 99
GCF of 22 and 99 is the largest possible number that divides 22 and 99 exactly without any remainder. The factors of 22 and 99 are 1, 2, 11, 22 and 1, 3, 9, 11, 33, 99 respectively. There are 3 commonly used methods to find the GCF of 22 and 99 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 22 and 99 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 22 and 99?
Answer: GCF of 22 and 99 is 11.
Explanation:
The GCF of two non-zero integers, x(22) and y(99), is the greatest positive integer m(11) that divides both x(22) and y(99) without any remainder.
Methods to Find GCF of 22 and 99
The methods to find the GCF of 22 and 99 are explained below.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
GCF of 22 and 99 by Prime Factorization
Prime factorization of 22 and 99 is (2 × 11) and (3 × 3 × 11) respectively. As visible, 22 and 99 have only one common prime factor i.e. 11. Hence, the GCF of 22 and 99 is 11.
GCF of 22 and 99 by Listing Common Factors
- Factors of 22: 1, 2, 11, 22
- Factors of 99: 1, 3, 9, 11, 33, 99
There are 2 common factors of 22 and 99, that are 1 and 11. Therefore, the greatest common factor of 22 and 99 is 11.
GCF of 22 and 99 by Long Division
GCF of 22 and 99 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 99 (larger number) by 22 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (22) by the remainder (11).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (11) is the GCF of 22 and 99.
☛ Also Check:
- GCF of 75, 8 and 21 = 1
- GCF of 63 and 81 = 9
- GCF of 64 and 144 = 16
- GCF of 54 and 90 = 18
- GCF of 30 and 50 = 10
- GCF of 60 and 100 = 20
- GCF of 2 and 8 = 2
FAQs on GCF of 22 and 99
What is the GCF of 22 and 99?
The GCF of 22 and 99 is 11. To calculate the greatest common factor (GCF) of 22 and 99, we need to factor each number (factors of 22 = 1, 2, 11, 22; factors of 99 = 1, 3, 9, 11, 33, 99) and choose the greatest factor that exactly divides both 22 and 99, i.e., 11.
What is the Relation Between LCM and GCF of 22, 99?
The following equation can be used to express the relation between Least Common Multiple and GCF of 22 and 99, i.e. GCF × LCM = 22 × 99.
How to Find the GCF of 22 and 99 by Long Division Method?
To find the GCF of 22, 99 using long division method, 99 is divided by 22. The corresponding divisor (11) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 22 and 99?
There are three commonly used methods to find the GCF of 22 and 99.
- By Euclidean Algorithm
- By Long Division
- By Prime Factorization
If the GCF of 99 and 22 is 11, Find its LCM.
GCF(99, 22) × LCM(99, 22) = 99 × 22
Since the GCF of 99 and 22 = 11
⇒ 11 × LCM(99, 22) = 2178
Therefore, LCM = 198
☛ Greatest Common Factor Calculator
How to Find the GCF of 22 and 99 by Prime Factorization?
To find the GCF of 22 and 99, we will find the prime factorization of the given numbers, i.e. 22 = 2 × 11; 99 = 3 × 3 × 11.
⇒ Since 11 is the only common prime factor of 22 and 99. Hence, GCF (22, 99) = 11.
☛ What is a Prime Number?