HCF of 4, 8 and 12
HCF of 4, 8 and 12 is the largest possible number that divides 4, 8 and 12 exactly without any remainder. The factors of 4, 8 and 12 are (1, 2, 4), (1, 2, 4, 8) and (1, 2, 3, 4, 6, 12) respectively. There are 3 commonly used methods to find the HCF of 4, 8 and 12  prime factorization, long division, and Euclidean algorithm.
1.  HCF of 4, 8 and 12 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 4, 8 and 12?
Answer: HCF of 4, 8 and 12 is 4.
Explanation:
The HCF of three nonzero integers, x(4), y(8) and z(12), is the highest positive integer m(4) that divides x(4), y(8) and z(12) without any remainder.
Methods to Find HCF of 4, 8 and 12
Let's look at the different methods for finding the HCF of 4, 8 and 12.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
HCF of 4, 8 and 12 by Listing Common Factors
 Factors of 4: 1, 2, 4
 Factors of 8: 1, 2, 4, 8
 Factors of 12: 1, 2, 3, 4, 6, 12
There are 3 common factors of 4, 8 and 12, that are 1, 2, and 4. Therefore, the highest common factor of 4, 8 and 12 is 4.
HCF of 4, 8 and 12 by Long Division
HCF of 4, 8 and 12 can be represented as HCF of (HCF of 4, 8) and 12. HCF(4, 8, 12) can be thus calculated by first finding HCF(4, 8) using long division and thereafter using this result with 12 to perform long division again.
 Step 1: Divide 8 (larger number) by 4 (smaller number).
 Step 2: Since the remainder = 0, the divisor (4) is the HCF(4, 8) = 4.
 Step 3: Now to find the HCF of 4 and 12, we will perform a long division on 12 and 4.
 Step 4: For remainder = 0, divisor = 4 ⇒ HCF(4, 12) = 4
Thus, HCF(4, 8, 12) = HCF(HCF(4, 8), 12) = 4.
HCF of 4, 8 and 12 by Prime Factorization
Prime factorization of 4, 8 and 12 is (2 × 2), (2 × 2 × 2) and (2 × 2 × 3) respectively. As visible, 4, 8 and 12 have common prime factors. Hence, the HCF of 4, 8 and 12 is 2 × 2 = 4.
☛ Also Check:
 HCF of 145 and 232 = 29
 HCF of 3 and 5 = 1
 HCF of 95 and 152 = 19
 HCF of 40, 60 and 75 = 5
 HCF of 8 and 15 = 1
 HCF of 240 and 6552 = 24
 HCF of 117 and 221 = 13
HCF of 4, 8 and 12 Examples

Example 1: Calculate the HCF of 4, 8, and 12 using LCM of the given numbers.
Solution:
Prime factorization of 4, 8 and 12 is given as,
 4 = 2 × 2
 8 = 2 × 2 × 2
 12 = 2 × 2 × 3
LCM(4, 8) = 8, LCM(8, 12) = 24, LCM(12, 4) = 12, LCM(4, 8, 12) = 24
⇒ HCF(4, 8, 12) = [(4 × 8 × 12) × LCM(4, 8, 12)]/[LCM(4, 8) × LCM (8, 12) × LCM(12, 4)]
⇒ HCF(4, 8, 12) = (384 × 24)/(8 × 24 × 12)
⇒ HCF(4, 8, 12) = 4.
Therefore, the HCF of 4, 8 and 12 is 4. 
Example 2: Find the highest number that divides 4, 8, and 12 completely.
Solution:
The highest number that divides 4, 8, and 12 exactly is their highest common factor.
 Factors of 4 = 1, 2, 4
 Factors of 8 = 1, 2, 4, 8
 Factors of 12 = 1, 2, 3, 4, 6, 12
The HCF of 4, 8, and 12 is 4.
∴ The highest number that divides 4, 8, and 12 is 4. 
Example 3: Verify the relation between the LCM and HCF of 4, 8 and 12.
Solution:
The relation between the LCM and HCF of 4, 8 and 12 is given as, HCF(4, 8, 12) = [(4 × 8 × 12) × LCM(4, 8, 12)]/[LCM(4, 8) × LCM (8, 12) × LCM(4, 12)]
⇒ Prime factorization of 4, 8 and 12: 4 = 2 × 2
 8 = 2 × 2 × 2
 12 = 2 × 2 × 3
∴ LCM of (4, 8), (8, 12), (4, 12), and (4, 8, 12) is 8, 24, 12, and 24 respectively.
Now, LHS = HCF(4, 8, 12) = 4.
And, RHS = [(4 × 8 × 12) × LCM(4, 8, 12)]/[LCM(4, 8) × LCM (8, 12) × LCM(4, 12)] = [(384) × 24]/[8 × 24 × 12]
LHS = RHS = 4.
Hence verified.
FAQs on HCF of 4, 8 and 12
What is the HCF of 4, 8 and 12?
The HCF of 4, 8 and 12 is 4. To calculate the HCF (Highest Common Factor) of 4, 8 and 12, we need to factor each number (factors of 4 = 1, 2, 4; factors of 8 = 1, 2, 4, 8; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the highest factor that exactly divides 4, 8 and 12, i.e., 4.
How to Find the HCF of 4, 8 and 12 by Prime Factorization?
To find the HCF of 4, 8 and 12, we will find the prime factorization of given numbers, i.e. 4 = 2 × 2; 8 = 2 × 2 × 2; 12 = 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 4, 8 and 12. Hence, HCF(4, 8, 12) = 2 × 2 = 4
☛ What is a Prime Number?
What is the Relation Between LCM and HCF of 4, 8 and 12?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 4, 8 and 12, i.e. HCF(4, 8, 12) = [(4 × 8 × 12) × LCM(4, 8, 12)]/[LCM(4, 8) × LCM (8, 12) × LCM(4, 12)].
☛ Highest Common Factor Calculator
Which of the following is HCF of 4, 8 and 12? 4, 35, 38, 38, 60, 55, 24, 59
HCF of 4, 8, 12 will be the number that divides 4, 8, and 12 without leaving any remainder. The only number that satisfies the given condition is 4.
What are the Methods to Find HCF of 4, 8 and 12?
There are three commonly used methods to find the HCF of 4, 8 and 12.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
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