Gcf For 12 And 15
GCF of 12 and xv
GCF of 12 and 15 is the largest possible number that divides 12 and 15 exactly without whatever remainder. The factors of 12 and fifteen are 1, 2, three, 4, half dozen, 12 and 1, three, 5, 15 respectively. There are three commonly used methods to find the GCF of 12 and 15 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 12 and 15 |
| 2. | List of Methods |
| 3. | Solved Examples |
| iv. | FAQs |
What is GCF of 12 and 15?
Answer: GCF of 12 and 15 is 3.
Explanation:
The GCF of two not-zero integers, x(12) and y(fifteen), is the greatest positive integer m(3) that divides both x(12) and y(fifteen) without any remainder.
Methods to Find GCF of 12 and 15
Let'southward expect at the unlike methods for finding the GCF of 12 and 15.
- Using Euclid'due south Algorithm
- Long Division Method
- Prime Factorization Method
GCF of 12 and fifteen by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and modernistic is the modulo operator.
Here Ten = 15 and Y = 12
- GCF(15, 12) = GCF(12, xv mod 12) = GCF(12, 3)
- GCF(12, 3) = GCF(3, 12 mod 3) = GCF(3, 0)
- GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where 10 ≠ 0)
Therefore, the value of GCF of 12 and 15 is three.
GCF of 12 and 15 by Long Division
GCF of 12 and xv is the divisor that nosotros go when the residue becomes 0 after doing long division repeatedly.
- Step one: Divide 15 (larger number) by 12 (smaller number).
- Step two: Since the rest ≠ 0, we volition divide the divisor of step 1 (12) by the rest (3).
- Stride iii: Repeat this process until the remainder = 0.
The corresponding divisor (3) is the GCF of 12 and fifteen.
GCF of 12 and fifteen by Prime Factorization
Prime factorization of 12 and 15 is (two × 2 × 3) and (3 × 5) respectively. As visible, 12 and 15 have only 1 mutual prime factor i.due east. 3. Hence, the GCF of 12 and fifteen is 3.
☛ Also Bank check:
- GCF of 8 and 12 = 4
- GCF of 28 and 72 = 4
- GCF of 12 and 18 = half-dozen
- GCF of fourteen and 15 = 1
- GCF of 27 and 63 = 9
- GCF of 7 and 35 = 7
- GCF of 18 and 35 = 1
GCF of 12 and fifteen Examples
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FAQs on GCF of 12 and 15
What is the GCF of 12 and 15?
The GCF of 12 and 15 is 3 . To calculate the GCF (Greatest Common Gene) of 12 and 15, nosotros need to factor each number (factors of 12 = 1, 2, 3, 4, half-dozen, 12; factors of 15 = ane, 3, 5, 15) and cull the greatest factor that exactly divides both 12 and 15, i.e., 3.
How to Find the GCF of 12 and 15 by Prime Factorization?
To find the GCF of 12 and 15, we will find the prime number factorization of the given numbers, i.e. 12 = 2 × ii × 3; 15 = 3 × v.
⇒ Since three is the only common prime factor of 12 and 15. Hence, GCF (12, xv) = three.
☛ Prime Numbers
If the GCF of 15 and 12 is 3, Detect its LCM.
GCF(xv, 12) × LCM(xv, 12) = 15 × 12
Since the GCF of 15 and 12 = iii
⇒ 3 × LCM(15, 12) = 180
Therefore, LCM = sixty
☛ GCF Calculator
What are the Methods to Find GCF of 12 and 15?
At that place are three ordinarily used methods to find the GCF of 12 and fifteen.
- By Prime Factorization
- Past Euclidean Algorithm
- By Long Division
How to Find the GCF of 12 and fifteen past Long Partition Method?
To find the GCF of 12, fifteen using long division method, xv is divided past 12. The corresponding divisor (3) when remainder equals 0 is taken as GCF.
What is the Relation Betwixt LCM and GCF of 12, fifteen?
The post-obit equation can exist used to express the relation between LCM and GCF of 12 and xv, i.e. GCF × LCM = 12 × 15.
Gcf For 12 And 15,
Source: https://www.cuemath.com/numbers/gcf-of-12-and-15/#:~:text=Therefore%2C%20the%20greatest%20common%20factor%20of%2012%20and%2015%20is%203.
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