HCF of 3 and 12
HCF of 3 and 12 is the largest possible number that divides 3 and 12 exactly without any remainder. The factors of 3 and 12 are 1, 3 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the HCF of 3 and 12 - long division, prime factorization, and Euclidean algorithm.
| 1. | HCF of 3 and 12 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 3 and 12?
Answer: HCF of 3 and 12 is 3.
Explanation:
The HCF of two non-zero integers, x(3) and y(12), is the highest positive integer m(3) that divides both x(3) and y(12) without any remainder.
Methods to Find HCF of 3 and 12
The methods to find the HCF of 3 and 12 are explained below.
- Long Division Method
- Using Euclid's Algorithm
- Prime Factorization Method
HCF of 3 and 12 by Long Division
HCF of 3 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 3 (smaller number).
- Step 2: Since the remainder = 0, the divisor (3) is the HCF of 3 and 12.
The corresponding divisor (3) is the HCF of 3 and 12.
HCF of 3 and 12 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 12 and Y = 3
- HCF(12, 3) = HCF(3, 12 mod 3) = HCF(3, 0)
- HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 3 and 12 is 3.
HCF of 3 and 12 by Prime Factorization
Prime factorization of 3 and 12 is (3) and (2 × 2 × 3) respectively. As visible, 3 and 12 have only one common prime factor i.e. 3. Hence, the HCF of 3 and 12 is 3.
☛ Also Check:
- HCF of 64 and 72 = 8
- HCF of 204, 1190 and 1445 = 17
- HCF of 32 and 40 = 8
- HCF of 1001 and 910 = 91
- HCF of 6, 72 and 120 = 6
- HCF of 120 and 75 = 15
- HCF of 96 and 120 = 24
FAQs on HCF of 3 and 12
What is the HCF of 3 and 12?
The HCF of 3 and 12 is 3. To calculate the HCF (Highest Common Factor) of 3 and 12, we need to factor each number (factors of 3 = 1, 3; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the highest factor that exactly divides both 3 and 12, i.e., 3.
What is the Relation Between LCM and HCF of 3, 12?
The following equation can be used to express the relation between Least Common Multiple and HCF of 3 and 12, i.e. HCF × LCM = 3 × 12.
What are the Methods to Find HCF of 3 and 12?
There are three commonly used methods to find the HCF of 3 and 12.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
If the HCF of 12 and 3 is 3, Find its LCM.
HCF(12, 3) × LCM(12, 3) = 12 × 3
Since the HCF of 12 and 3 = 3
⇒ 3 × LCM(12, 3) = 36
Therefore, LCM = 12
☛ HCF Calculator
How to Find the HCF of 3 and 12 by Long Division Method?
To find the HCF of 3, 12 using long division method, 12 is divided by 3. The corresponding divisor (3) when remainder equals 0 is taken as HCF.
How to Find the HCF of 3 and 12 by Prime Factorization?
To find the HCF of 3 and 12, we will find the prime factorization of the given numbers, i.e. 3 = 3; 12 = 2 × 2 × 3.
⇒ Since 3 is the only common prime factor of 3 and 12. Hence, HCF (3, 12) = 3.
☛ What are Prime Numbers?