HCF of 12, 36 and 48
HCF of 12, 36 and 48 is the largest possible number that divides 12, 36 and 48 exactly without any remainder. The factors of 12, 36 and 48 are (1, 2, 3, 4, 6, 12), (1, 2, 3, 4, 6, 9, 12, 18, 36) and (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) respectively. There are 3 commonly used methods to find the HCF of 12, 36 and 48  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 12, 36 and 48 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 12, 36 and 48?
Answer: HCF of 12, 36 and 48 is 12.
Explanation:
The HCF of three nonzero integers, x(12), y(36) and z(48), is the highest positive integer m(12) that divides x(12), y(36) and z(48) without any remainder.
Methods to Find HCF of 12, 36 and 48
Let's look at the different methods for finding the HCF of 12, 36 and 48.
 Using Euclid's Algorithm
 Prime Factorization Method
 Listing Common Factors
HCF of 12, 36 and 48 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.
HCF(12, 36, 48) = HCF(HCF(12, 36), 48)
 HCF(36, 12) = HCF(12, 36 mod 12) = HCF(12, 0)
 HCF(12, 0) = 12 (∵ HCF(X, 0) = X, where X ≠ 0)
Steps for HCF(12, 48)
 HCF(48, 12) = HCF(12, 48 mod 12) = HCF(12, 0)
 HCF(12, 0) = 12 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 12, 36 and 48 is 12.
HCF of 12, 36 and 48 by Prime Factorization
Prime factorization of 12, 36 and 48 is (2 × 2 × 3), (2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 12, 36 and 48 have common prime factors. Hence, the HCF of 12, 36 and 48 is 2 × 2 × 3 = 12.
HCF of 12, 36 and 48 by Listing Common Factors
 Factors of 12: 1, 2, 3, 4, 6, 12
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
There are 6 common factors of 12, 36 and 48, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 12, 36 and 48 is 12.
☛ Also Check:
 HCF of 18 and 24 = 6
 HCF of 240 and 6552 = 24
 HCF of 36 and 42 = 6
 HCF of 396 and 1080 = 36
 HCF of 90 and 120 = 30
 HCF of 36 and 90 = 18
 HCF of 4 and 8 = 4
HCF of 12, 36 and 48 Examples

Example 1: Verify the relation between the LCM and HCF of 12, 36 and 48.
Solution:
The relation between the LCM and HCF of 12, 36 and 48 is given as, HCF(12, 36, 48) = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(12, 48)]
⇒ Prime factorization of 12, 36 and 48: 12 = 2 × 2 × 3
 36 = 2 × 2 × 3 × 3
 48 = 2 × 2 × 2 × 2 × 3
∴ LCM of (12, 36), (36, 48), (12, 48), and (12, 36, 48) is 36, 144, 48, and 144 respectively.
Now, LHS = HCF(12, 36, 48) = 12.
And, RHS = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(12, 48)] = [(20736) × 144]/[36 × 144 × 48]
LHS = RHS = 12.
Hence verified. 
Example 2: Find the highest number that divides 12, 36, and 48 completely.
Solution:
The highest number that divides 12, 36, and 48 exactly is their highest common factor.
 Factors of 12 = 1, 2, 3, 4, 6, 12
 Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The HCF of 12, 36, and 48 is 12.
∴ The highest number that divides 12, 36, and 48 is 12. 
Example 3: Calculate the HCF of 12, 36, and 48 using LCM of the given numbers.
Solution:
Prime factorization of 12, 36 and 48 is given as,
 12 = 2 × 2 × 3
 36 = 2 × 2 × 3 × 3
 48 = 2 × 2 × 2 × 2 × 3
LCM(12, 36) = 36, LCM(36, 48) = 144, LCM(48, 12) = 48, LCM(12, 36, 48) = 144
⇒ HCF(12, 36, 48) = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(48, 12)]
⇒ HCF(12, 36, 48) = (20736 × 144)/(36 × 144 × 48)
⇒ HCF(12, 36, 48) = 12.
Therefore, the HCF of 12, 36 and 48 is 12.
FAQs on HCF of 12, 36 and 48
What is the HCF of 12, 36 and 48?
The HCF of 12, 36 and 48 is 12. To calculate the highest common factor of 12, 36 and 48, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the highest factor that exactly divides 12, 36 and 48, i.e., 12.
How to Find the HCF of 12, 36 and 48 by Prime Factorization?
To find the HCF of 12, 36 and 48, we will find the prime factorization of given numbers, i.e. 12 = 2 × 2 × 3; 36 = 2 × 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 12, 36 and 48. Hence, HCF(12, 36, 48) = 2 × 2 × 3 = 12
☛ Prime Numbers
What are the Methods to Find HCF of 12, 36 and 48?
There are three commonly used methods to find the HCF of 12, 36 and 48.
 By Prime Factorization
 By Long Division
 By Listing Common Factors
Which of the following is HCF of 12, 36 and 48? 12, 89, 55, 63, 97, 55, 97
HCF of 12, 36, 48 will be the number that divides 12, 36, and 48 without leaving any remainder. The only number that satisfies the given condition is 12.
What is the Relation Between LCM and HCF of 12, 36 and 48?
The following equation can be used to express the relation between LCM and HCF of 12, 36 and 48, i.e. HCF(12, 36, 48) = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(12, 48)].
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