GCF of 7 and 12 is the largest possible number that divides 7 and 12 exactly without any remainder. The factors of 7 and 12 are 1, 7 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the GCF of 7 and 12 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 7 and 12 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 7 and 12?
Answer: GCF of 7 and 12 is 1.
Explanation:
The GCF of two non-zero integers, x(7) and y(12), is the greatest positive integer m(1) that divides both x(7) and y(12) without any remainder.
Methods to Find GCF of 7 and 12
Let's look at the different methods for finding the GCF of 7 and 12.
- Long Division Method
- Listing Common Factors
- Using Euclid's Algorithm
GCF of 7 and 12 by Long Division
GCF of 7 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 12 (larger number) by 7 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (7) by the remainder (5).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 7 and 12.
GCF of 7 and 12 by Listing Common Factors
- Factors of 7: 1, 7
- Factors of 12: 1, 2, 3, 4, 6, 12
Since, 1 is the only common factor between 7 and 12. The Greatest Common Factor of 7 and 12 is 1.
GCF of 7 and 12 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 12 and Y = 7
- GCF(12, 7) = GCF(7, 12 mod 7) = GCF(7, 5)
- GCF(7, 5) = GCF(5, 7 mod 5) = GCF(5, 2)
- GCF(5, 2) = GCF(2, 5 mod 2) = GCF(2, 1)
- GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)
Therefore, the value of GCF of 7 and 12 is 1.
☛ Also Check:
- GCF of 6 and 36 = 6
- GCF of 75 and 90 = 15
- GCF of 75 and 125 = 25
- GCF of 60 and 80 = 20
- GCF of 84 and 42 = 42
- GCF of 86 and 42 = 2
- GCF of 16 and 25 = 1
GCF of 7 and 12 Examples
Example 1: The product of two numbers is 84. If their GCF is 1, what is their LCM?
Solution:
Given: GCF = 1 and product of numbers = 84
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 84/1
Therefore, the LCM is 84.Example 2: Find the greatest number that divides 7 and 12 exactly.
Solution:
The greatest number that divides 7 and 12 exactly is their greatest common factor, i.e. GCF of 7 and 12.
⇒ Factors of 7 and 12:- Factors of 7 = 1, 7
- Factors of 12 = 1, 2, 3, 4, 6, 12
Therefore, the GCF of 7 and 12 is 1.
Example 3: Find the GCF of 7 and 12, if their LCM is 84.
Solution:
∵ LCM × GCF = 7 × 12
⇒ GCF(7, 12) = (7 × 12)/84 = 1
Therefore, the greatest common factor of 7 and 12 is 1.
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FAQs on GCF of 7 and 12
What is the GCF of 7 and 12?
The GCF of 7 and 12 is 1. To calculate the greatest common factor (GCF) of 7 and 12, we need to factor each number (factors of 7 = 1, 7; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 7 and 12, i.e., 1.
How to Find the GCF of 7 and 12 by Long Division Method?
To find the GCF of 7, 12 using long division method, 12 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
If the GCF of 12 and 7 is 1, Find its LCM.
GCF(12, 7) × LCM(12, 7) = 12 × 7
Since the GCF of 12 and 7 = 1
⇒ 1 × LCM(12, 7) = 84
Therefore, LCM = 84
☛ GCF Calculator
What is the Relation Between LCM and GCF of 7, 12?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 7 and 12, i.e. GCF × LCM = 7 × 12.
What are the Methods to Find GCF of 7 and 12?
There are three commonly used methods to find the GCF of 7 and 12.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
How to Find the GCF of 7 and 12 by Prime Factorization?
To find the GCF of 7 and 12, we will find the prime factorization of the given numbers, i.e. 7 = 7; 12 = 2 × 2 × 3.
⇒ There is no common prime factor for 7 and 12. Hence, GCF (7, 12) = 1.
☛ Prime Number
