GCF of 55 and 121
GCF of 55 and 121 is the largest possible number that divides 55 and 121 exactly without any remainder. The factors of 55 and 121 are 1, 5, 11, 55 and 1, 11, 121 respectively. There are 3 commonly used methods to find the GCF of 55 and 121 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 55 and 121 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 55 and 121?
Answer: GCF of 55 and 121 is 11.
Explanation:
The GCF of two non-zero integers, x(55) and y(121), is the greatest positive integer m(11) that divides both x(55) and y(121) without any remainder.
Methods to Find GCF of 55 and 121
Let's look at the different methods for finding the GCF of 55 and 121.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 55 and 121 by Listing Common Factors
- Factors of 55: 1, 5, 11, 55
- Factors of 121: 1, 11, 121
There are 2 common factors of 55 and 121, that are 1 and 11. Therefore, the greatest common factor of 55 and 121 is 11.
GCF of 55 and 121 by Long Division
GCF of 55 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 55 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (55) by the remainder (11).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (11) is the GCF of 55 and 121.
GCF of 55 and 121 by Prime Factorization
Prime factorization of 55 and 121 is (5 × 11) and (11 × 11) respectively. As visible, 55 and 121 have only one common prime factor i.e. 11. Hence, the GCF of 55 and 121 is 11.
☛ Also Check:
- GCF of 50 and 80 = 10
- GCF of 15 and 40 = 5
- GCF of 13 and 39 = 13
- GCF of 5 and 10 = 5
- GCF of 27 and 45 = 9
- GCF of 20 and 70 = 10
- GCF of 56 and 70 = 14
FAQs on GCF of 55 and 121
What is the GCF of 55 and 121?
The GCF of 55 and 121 is 11. To calculate the GCF (Greatest Common Factor) of 55 and 121, we need to factor each number (factors of 55 = 1, 5, 11, 55; factors of 121 = 1, 11, 121) and choose the greatest factor that exactly divides both 55 and 121, i.e., 11.
What are the Methods to Find GCF of 55 and 121?
There are three commonly used methods to find the GCF of 55 and 121.
- By Euclidean Algorithm
- By Prime Factorization
- By Long Division
How to Find the GCF of 55 and 121 by Long Division Method?
To find the GCF of 55, 121 using long division method, 121 is divided by 55. The corresponding divisor (11) when remainder equals 0 is taken as GCF.
If the GCF of 121 and 55 is 11, Find its LCM.
GCF(121, 55) × LCM(121, 55) = 121 × 55
Since the GCF of 121 and 55 = 11
⇒ 11 × LCM(121, 55) = 6655
Therefore, LCM = 605
☛ Greatest Common Factor Calculator
How to Find the GCF of 55 and 121 by Prime Factorization?
To find the GCF of 55 and 121, we will find the prime factorization of the given numbers, i.e. 55 = 5 × 11; 121 = 11 × 11.
⇒ Since 11 is the only common prime factor of 55 and 121. Hence, GCF (55, 121) = 11.
☛ Prime Numbers
What is the Relation Between LCM and GCF of 55, 121?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 55 and 121, i.e. GCF × LCM = 55 × 121.