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HCF of 12576 and 4052

HCF of 12576 and 4052 is the largest possible number that divides 12576 and 4052 exactly without any remainder. The factors of 12576 and 4052 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 131, 262, 393, 524, 786, 1048, 1572, 2096, 3144, 4192, 6288, 12576 and 1, 2, 4, 1013, 2026, 4052 respectively. There are 3 commonly used methods to find the HCF of 12576 and 4052 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 12576 and 4052
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12576 and 4052?

Answer: HCF of 12576 and 4052 is 4.

Explanation:

The HCF of two non-zero integers, x(12576) and y(4052), is the highest positive integer m(4) that divides both x(12576) and y(4052) without any remainder.

Methods to Find HCF of 12576 and 4052

The methods to find the HCF of 12576 and 4052 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

HCF of 12576 and 4052 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 = 12576 and Y = 4052

HCF(12576, 4052) = HCF(4052, 12576 mod 4052) = HCF(4052, 420)
HCF(4052, 420) = HCF(420, 4052 mod 420) = HCF(420, 272)
HCF(420, 272) = HCF(272, 420 mod 272) = HCF(272, 148)
HCF(272, 148) = HCF(148, 272 mod 148) = HCF(148, 124)
HCF(148, 124) = HCF(124, 148 mod 124) = HCF(124, 24)
HCF(124, 24) = HCF(24, 124 mod 24) = HCF(24, 4)
HCF(24, 4) = HCF(4, 24 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12576 and 4052 is 4.

HCF of 12576 and 4052 by Prime Factorization

Prime factorization of 12576 and 4052 is (2 × 2 × 2 × 2 × 2 × 3 × 131) and (2 × 2 × 1013) respectively. As visible, 12576 and 4052 have common prime factors. Hence, the HCF of 12576 and 4052 is 2 × 2 = 4.

HCF of 12576 and 4052 by Listing Common Factors

Factors of 12576: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 131, 262, 393, 524, 786, 1048, 1572, 2096, 3144, 4192, 6288, 12576
Factors of 4052: 1, 2, 4, 1013, 2026, 4052

There are 3 common factors of 12576 and 4052, that are 1, 2, and 4. Therefore, the highest common factor of 12576 and 4052 is 4.

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HCF of 12576 and 4052 Examples

Example 1: Find the highest number that divides 12576 and 4052 exactly.

Solution:

The highest number that divides 12576 and 4052 exactly is their highest common factor, i.e. HCF of 12576 and 4052.
⇒ Factors of 12576 and 4052:
- Factors of 12576 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 131, 262, 393, 524, 786, 1048, 1572, 2096, 3144, 4192, 6288, 12576
- Factors of 4052 = 1, 2, 4, 1013, 2026, 4052
Therefore, the HCF of 12576 and 4052 is 4.
Example 2: For two numbers, HCF = 4 and LCM = 12739488. If one number is 4052, find the other number.

Solution:

Given: HCF (z, 4052) = 4 and LCM (z, 4052) = 12739488
∵ HCF × LCM = 4052 × (z)
⇒ z = (HCF × LCM)/4052
⇒ z = (4 × 12739488)/4052
⇒ z = 12576
Therefore, the other number is 12576.
Example 3: Find the HCF of 12576 and 4052, if their LCM is 12739488.

Solution:

∵ LCM × HCF = 12576 × 4052
⇒ HCF(12576, 4052) = (12576 × 4052)/12739488 = 4
Therefore, the highest common factor of 12576 and 4052 is 4.

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FAQs on HCF of 12576 and 4052

What is the HCF of 12576 and 4052?

The HCF of 12576 and 4052 is 4. To calculate the HCF (Highest Common Factor) of 12576 and 4052, we need to factor each number (factors of 12576 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 131, 262, 393, 524, 786, 1048, 1572, 2096, 3144, 4192, 6288, 12576; factors of 4052 = 1, 2, 4, 1013, 2026, 4052) and choose the highest factor that exactly divides both 12576 and 4052, i.e., 4.

How to Find the HCF of 12576 and 4052 by Long Division Method?

To find the HCF of 12576, 4052 using long division method, 12576 is divided by 4052. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

If the HCF of 4052 and 12576 is 4, Find its LCM.

HCF(4052, 12576) × LCM(4052, 12576) = 4052 × 12576
Since the HCF of 4052 and 12576 = 4
⇒ 4 × LCM(4052, 12576) = 50957952
Therefore, LCM = 12739488
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 12576 and 4052?

There are three commonly used methods to find the HCF of 12576 and 4052.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and HCF of 12576, 4052?

The following equation can be used to express the relation between Least Common Multiple and HCF of 12576 and 4052, i.e. HCF × LCM = 12576 × 4052.

How to Find the HCF of 12576 and 4052 by Prime Factorization?

To find the HCF of 12576 and 4052, we will find the prime factorization of the given numbers, i.e. 12576 = 2 × 2 × 2 × 2 × 2 × 3 × 131; 4052 = 2 × 2 × 1013.
⇒ Since 2, 2 are common terms in the prime factorization of 12576 and 4052. Hence, HCF(12576, 4052) = 2 × 2 = 4
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