GCF of 44 and 121 is the largest possible number that divides 44 and 121 exactly without any remainder. The factors of 44 and 121 are 1, 2, 4, 11, 22, 44 and 1, 11, 121 respectively. There are 3 commonly used methods to find the GCF of 44 and 121 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 44 and 121 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 44 and 121?
Answer: GCF of 44 and 121 is 11.
Explanation:
The GCF of two non-zero integers, x(44) and y(121), is the greatest positive integer m(11) that divides both x(44) and y(121) without any remainder.
Methods to Find GCF of 44 and 121
Let's look at the different methods for finding the GCF of 44 and 121.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 44 and 121 by Long Division
GCF of 44 and 121 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 121 (larger number) by 44 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (44) by the remainder (33).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (11) is the GCF of 44 and 121.
GCF of 44 and 121 by Prime Factorization
Prime factorization of 44 and 121 is (2 × 2 × 11) and (11 × 11) respectively. As visible, 44 and 121 have only one common prime factor i.e. 11. Hence, the GCF of 44 and 121 is 11.
GCF of 44 and 121 by Listing Common Factors
- Factors of 44: 1, 2, 4, 11, 22, 44
- Factors of 121: 1, 11, 121
There are 2 common factors of 44 and 121, that are 1 and 11. Therefore, the greatest common factor of 44 and 121 is 11.
☛ Also Check:
- GCF of 24 and 60 = 12
- GCF of 15 and 45 = 15
- GCF of 60 and 20 = 20
- GCF of 51 and 85 = 17
- GCF of 10 and 16 = 2
- GCF of 28 and 42 = 14
- GCF of 15 and 30 = 15
GCF of 44 and 121 Examples
Example 1: The product of two numbers is 5324. If their GCF is 11, what is their LCM?
Solution:
Given: GCF = 11 and product of numbers = 5324
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5324/11
Therefore, the LCM is 484.Example 2: Find the GCF of 44 and 121, if their LCM is 484.
Solution:
∵ LCM × GCF = 44 × 121
⇒ GCF(44, 121) = (44 × 121)/484 = 11
Therefore, the greatest common factor of 44 and 121 is 11.Example 3: For two numbers, GCF = 11 and LCM = 484. If one number is 44, find the other number.
Solution:
Given: GCF (x, 44) = 11 and LCM (x, 44) = 484
∵ GCF × LCM = 44 × (x)
⇒ x = (GCF × LCM)/44
⇒ x = (11 × 484)/44
⇒ x = 121
Therefore, the other number is 121.
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FAQs on GCF of 44 and 121
What is the GCF of 44 and 121?
The GCF of 44 and 121 is 11. To calculate the GCF of 44 and 121, we need to factor each number (factors of 44 = 1, 2, 4, 11, 22, 44; factors of 121 = 1, 11, 121) and choose the greatest factor that exactly divides both 44 and 121, i.e., 11.
What are the Methods to Find GCF of 44 and 121?
There are three commonly used methods to find the GCF of 44 and 121.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
If the GCF of 121 and 44 is 11, Find its LCM.
GCF(121, 44) × LCM(121, 44) = 121 × 44
Since the GCF of 121 and 44 = 11
⇒ 11 × LCM(121, 44) = 5324
Therefore, LCM = 484
☛ GCF Calculator
What is the Relation Between LCM and GCF of 44, 121?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 44 and 121, i.e. GCF × LCM = 44 × 121.
How to Find the GCF of 44 and 121 by Prime Factorization?
To find the GCF of 44 and 121, we will find the prime factorization of the given numbers, i.e. 44 = 2 × 2 × 11; 121 = 11 × 11.
⇒ Since 11 is the only common prime factor of 44 and 121. Hence, GCF (44, 121) = 11.
☛ What are Prime Numbers?
How to Find the GCF of 44 and 121 by Long Division Method?
To find the GCF of 44, 121 using long division method, 121 is divided by 44. The corresponding divisor (11) when remainder equals 0 is taken as GCF.
