GCF of 39 and 91
GCF of 39 and 91 is the largest possible number that divides 39 and 91 exactly without any remainder. The factors of 39 and 91 are 1, 3, 13, 39 and 1, 7, 13, 91 respectively. There are 3 commonly used methods to find the GCF of 39 and 91 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 39 and 91 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 39 and 91?
Answer: GCF of 39 and 91 is 13.
Explanation:
The GCF of two non-zero integers, x(39) and y(91), is the greatest positive integer m(13) that divides both x(39) and y(91) without any remainder.
Methods to Find GCF of 39 and 91
Let's look at the different methods for finding the GCF of 39 and 91.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 39 and 91 by Listing Common Factors
- Factors of 39: 1, 3, 13, 39
- Factors of 91: 1, 7, 13, 91
There are 2 common factors of 39 and 91, that are 1 and 13. Therefore, the greatest common factor of 39 and 91 is 13.
GCF of 39 and 91 by Long Division
GCF of 39 and 91 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 91 (larger number) by 39 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (39) by the remainder (13).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (13) is the GCF of 39 and 91.
GCF of 39 and 91 by Prime Factorization
Prime factorization of 39 and 91 is (3 × 13) and (7 × 13) respectively. As visible, 39 and 91 have only one common prime factor i.e. 13. Hence, the GCF of 39 and 91 is 13.
☛ Also Check:
- GCF of 7 and 14 = 7
- GCF of 20 and 100 = 20
- GCF of 25 and 55 = 5
- GCF of 64 and 32 = 32
- GCF of 42 and 70 = 14
- GCF of 60 and 84 = 12
- GCF of 27 and 72 = 9
FAQs on GCF of 39 and 91
What is the GCF of 39 and 91?
The GCF of 39 and 91 is 13. To calculate the GCF (Greatest Common Factor) of 39 and 91, we need to factor each number (factors of 39 = 1, 3, 13, 39; factors of 91 = 1, 7, 13, 91) and choose the greatest factor that exactly divides both 39 and 91, i.e., 13.
How to Find the GCF of 39 and 91 by Prime Factorization?
To find the GCF of 39 and 91, we will find the prime factorization of the given numbers, i.e. 39 = 3 × 13; 91 = 7 × 13.
⇒ Since 13 is the only common prime factor of 39 and 91. Hence, GCF (39, 91) = 13.
☛ Prime Number
What is the Relation Between LCM and GCF of 39, 91?
The following equation can be used to express the relation between Least Common Multiple and GCF of 39 and 91, i.e. GCF × LCM = 39 × 91.
If the GCF of 91 and 39 is 13, Find its LCM.
GCF(91, 39) × LCM(91, 39) = 91 × 39
Since the GCF of 91 and 39 = 13
⇒ 13 × LCM(91, 39) = 3549
Therefore, LCM = 273
☛ GCF Calculator
How to Find the GCF of 39 and 91 by Long Division Method?
To find the GCF of 39, 91 using long division method, 91 is divided by 39. The corresponding divisor (13) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 39 and 91?
There are three commonly used methods to find the GCF of 39 and 91.
- By Listing Common Factors
- By Long Division
- By Prime Factorization