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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.

HCF of 2472 and 1284

Explanation:

The HCF of two non-zero 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

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.

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HCF of 2472 and 1284 Examples

  1. 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.

  2. 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.

  3. 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.

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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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