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HCF of 3556 and 3444

HCF of 3556 and 3444 is the largest possible number that divides 3556 and 3444 exactly without any remainder. The factors of 3556 and 3444 are 1, 2, 4, 7, 14, 28, 127, 254, 508, 889, 1778, 3556 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 41, 42, 82, 84, 123, 164, 246, 287, 492, 574, 861, 1148, 1722, 3444 respectively. There are 3 commonly used methods to find the HCF of 3556 and 3444 - long division, Euclidean algorithm, and prime factorization.

1. HCF of 3556 and 3444
2. List of Methods
3. Solved Examples
4. FAQs

What is HCF of 3556 and 3444?

Answer: HCF of 3556 and 3444 is 28.

HCF of 3556 and 3444

Explanation:

The HCF of two non-zero integers, x(3556) and y(3444), is the highest positive integer m(28) that divides both x(3556) and y(3444) without any remainder.

Methods to Find HCF of 3556 and 3444

The methods to find the HCF of 3556 and 3444 are explained below.

  • Using Euclid's Algorithm
  • Listing Common Factors
  • Prime Factorization Method

HCF of 3556 and 3444 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 = 3556 and Y = 3444

  • HCF(3556, 3444) = HCF(3444, 3556 mod 3444) = HCF(3444, 112)
  • HCF(3444, 112) = HCF(112, 3444 mod 112) = HCF(112, 84)
  • HCF(112, 84) = HCF(84, 112 mod 84) = HCF(84, 28)
  • HCF(84, 28) = HCF(28, 84 mod 28) = HCF(28, 0)
  • HCF(28, 0) = 28 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 3556 and 3444 is 28.

HCF of 3556 and 3444 by Listing Common Factors

HCF of 3556 and 3444 by Listing Common Factors
  • Factors of 3556: 1, 2, 4, 7, 14, 28, 127, 254, 508, 889, 1778, 3556
  • Factors of 3444: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 41, 42, 82, 84, 123, 164, 246, 287, 492, 574, 861, 1148, 1722, 3444

There are 6 common factors of 3556 and 3444, that are 1, 2, 4, 7, 14, and 28. Therefore, the highest common factor of 3556 and 3444 is 28.

HCF of 3556 and 3444 by Prime Factorization

Prime factorization of 3556 and 3444 is (2 × 2 × 7 × 127) and (2 × 2 × 3 × 7 × 41) respectively. As visible, 3556 and 3444 have common prime factors. Hence, the HCF of 3556 and 3444 is 2 × 2 × 7 = 28.

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HCF of 3556 and 3444 Examples

  1. Example 1: Find the highest number that divides 3556 and 3444 exactly.

    Solution:

    The highest number that divides 3556 and 3444 exactly is their highest common factor, i.e. HCF of 3556 and 3444.
    ⇒ Factors of 3556 and 3444:

    • Factors of 3556 = 1, 2, 4, 7, 14, 28, 127, 254, 508, 889, 1778, 3556
    • Factors of 3444 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 41, 42, 82, 84, 123, 164, 246, 287, 492, 574, 861, 1148, 1722, 3444

    Therefore, the HCF of 3556 and 3444 is 28.

  2. Example 2: Find the HCF of 3556 and 3444, if their LCM is 437388.

    Solution:

    ∵ LCM × HCF = 3556 × 3444
    ⇒ HCF(3556, 3444) = (3556 × 3444)/437388 = 28
    Therefore, the highest common factor of 3556 and 3444 is 28.

  3. Example 3: For two numbers, HCF = 28 and LCM = 437388. If one number is 3444, find the other number.

    Solution:

    Given: HCF (z, 3444) = 28 and LCM (z, 3444) = 437388
    ∵ HCF × LCM = 3444 × (z)
    ⇒ z = (HCF × LCM)/3444
    ⇒ z = (28 × 437388)/3444
    ⇒ z = 3556
    Therefore, the other number is 3556.

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FAQs on HCF of 3556 and 3444

What is the HCF of 3556 and 3444?

The HCF of 3556 and 3444 is 28. To calculate the Highest common factor of 3556 and 3444, we need to factor each number (factors of 3556 = 1, 2, 4, 7, 14, 28, 127, 254, 508, 889, 1778, 3556; factors of 3444 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 41, 42, 82, 84, 123, 164, 246, 287, 492, 574, 861, 1148, 1722, 3444) and choose the highest factor that exactly divides both 3556 and 3444, i.e., 28.

How to Find the HCF of 3556 and 3444 by Long Division Method?

To find the HCF of 3556, 3444 using long division method, 3556 is divided by 3444. The corresponding divisor (28) when remainder equals 0 is taken as HCF.

How to Find the HCF of 3556 and 3444 by Prime Factorization?

To find the HCF of 3556 and 3444, we will find the prime factorization of the given numbers, i.e. 3556 = 2 × 2 × 7 × 127; 3444 = 2 × 2 × 3 × 7 × 41.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 3556 and 3444. Hence, HCF(3556, 3444) = 2 × 2 × 7 = 28
☛ What are Prime Numbers?

What are the Methods to Find HCF of 3556 and 3444?

There are three commonly used methods to find the HCF of 3556 and 3444.

  • By Prime Factorization
  • By Long Division
  • By Euclidean Algorithm

If the HCF of 3444 and 3556 is 28, Find its LCM.

HCF(3444, 3556) × LCM(3444, 3556) = 3444 × 3556
Since the HCF of 3444 and 3556 = 28
⇒ 28 × LCM(3444, 3556) = 12246864
Therefore, LCM = 437388
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What is the Relation Between LCM and HCF of 3556, 3444?

The following equation can be used to express the relation between Least Common Multiple and HCF of 3556 and 3444, i.e. HCF × LCM = 3556 × 3444.

 
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