HCF of 2472 and 1284
HCF of 2472 and 1284 is the largest possible number that divides 2472 and 1284 exactly without any remainder. The factors of 2472 and 1284 are 1, 2, 3, 4, 6, 8, 12, 24, 103, 206, 309, 412, 618, 824, 1236, 2472 and 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284 respectively. There are 3 commonly used methods to find the HCF of 2472 and 1284  prime factorization, long division, and Euclidean algorithm.
1.  HCF of 2472 and 1284 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 2472 and 1284?
Answer: HCF of 2472 and 1284 is 12.
Explanation:
The HCF of two nonzero integers, x(2472) and y(1284), is the highest positive integer m(12) that divides both x(2472) and y(1284) without any remainder.
Methods to Find HCF of 2472 and 1284
The methods to find the HCF of 2472 and 1284 are explained below.
 Prime Factorization Method
 Using Euclid's Algorithm
 Listing Common Factors
HCF of 2472 and 1284 by Prime Factorization
Prime factorization of 2472 and 1284 is (2 × 2 × 2 × 3 × 103) and (2 × 2 × 3 × 107) respectively. As visible, 2472 and 1284 have common prime factors. Hence, the HCF of 2472 and 1284 is 2 × 2 × 3 = 12.
HCF of 2472 and 1284 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 = 2472 and Y = 1284
 HCF(2472, 1284) = HCF(1284, 2472 mod 1284) = HCF(1284, 1188)
 HCF(1284, 1188) = HCF(1188, 1284 mod 1188) = HCF(1188, 96)
 HCF(1188, 96) = HCF(96, 1188 mod 96) = HCF(96, 36)
 HCF(96, 36) = HCF(36, 96 mod 36) = HCF(36, 24)
 HCF(36, 24) = HCF(24, 36 mod 24) = HCF(24, 12)
 HCF(24, 12) = HCF(12, 24 mod 12) = HCF(12, 0)
 HCF(12, 0) = 12 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 2472 and 1284 is 12.
HCF of 2472 and 1284 by Listing Common Factors
 Factors of 2472: 1, 2, 3, 4, 6, 8, 12, 24, 103, 206, 309, 412, 618, 824, 1236, 2472
 Factors of 1284: 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284
There are 6 common factors of 2472 and 1284, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 2472 and 1284 is 12.
☛ Also Check:
 HCF of 4052 and 420 = 4
 HCF of 8 and 12 = 4
 HCF of 8, 9 and 25 = 1
 HCF of 16 and 36 = 4
 HCF of 120, 144 and 204 = 12
 HCF of 52 and 117 = 13
 HCF of 18 and 20 = 2
HCF of 2472 and 1284 Examples

Example 1: Find the HCF of 2472 and 1284, if their LCM is 264504.
Solution:
∵ LCM × HCF = 2472 × 1284
⇒ HCF(2472, 1284) = (2472 × 1284)/264504 = 12
Therefore, the highest common factor of 2472 and 1284 is 12. 
Example 2: For two numbers, HCF = 12 and LCM = 264504. If one number is 2472, find the other number.
Solution:
Given: HCF (x, 2472) = 12 and LCM (x, 2472) = 264504
∵ HCF × LCM = 2472 × (x)
⇒ x = (HCF × LCM)/2472
⇒ x = (12 × 264504)/2472
⇒ x = 1284
Therefore, the other number is 1284. 
Example 3: Find the highest number that divides 2472 and 1284 exactly.
Solution:
The highest number that divides 2472 and 1284 exactly is their highest common factor, i.e. HCF of 2472 and 1284.
⇒ Factors of 2472 and 1284: Factors of 2472 = 1, 2, 3, 4, 6, 8, 12, 24, 103, 206, 309, 412, 618, 824, 1236, 2472
 Factors of 1284 = 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284
Therefore, the HCF of 2472 and 1284 is 12.
FAQs on HCF of 2472 and 1284
What is the HCF of 2472 and 1284?
The HCF of 2472 and 1284 is 12. To calculate the Highest common factor (HCF) of 2472 and 1284, we need to factor each number (factors of 2472 = 1, 2, 3, 4, 6, 8, 12, 24, 103, 206, 309, 412, 618, 824, 1236, 2472; factors of 1284 = 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284) and choose the highest factor that exactly divides both 2472 and 1284, i.e., 12.
What are the Methods to Find HCF of 2472 and 1284?
There are three commonly used methods to find the HCF of 2472 and 1284.
 By Long Division
 By Prime Factorization
 By Listing Common Factors
How to Find the HCF of 2472 and 1284 by Prime Factorization?
To find the HCF of 2472 and 1284, we will find the prime factorization of the given numbers, i.e. 2472 = 2 × 2 × 2 × 3 × 103; 1284 = 2 × 2 × 3 × 107.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 2472 and 1284. Hence, HCF(2472, 1284) = 2 × 2 × 3 = 12
☛ Prime Numbers
What is the Relation Between LCM and HCF of 2472, 1284?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 2472 and 1284, i.e. HCF × LCM = 2472 × 1284.
How to Find the HCF of 2472 and 1284 by Long Division Method?
To find the HCF of 2472, 1284 using long division method, 2472 is divided by 1284. The corresponding divisor (12) when remainder equals 0 is taken as HCF.
If the HCF of 1284 and 2472 is 12, Find its LCM.
HCF(1284, 2472) × LCM(1284, 2472) = 1284 × 2472
Since the HCF of 1284 and 2472 = 12
⇒ 12 × LCM(1284, 2472) = 3174048
Therefore, LCM = 264504
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