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HCF of 1260 and 7344

HCF of 1260 and 7344 is the largest possible number that divides 1260 and 7344 exactly without any remainder. The factors of 1260 and 7344 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 34, 36, 48, 51, 54, 68, 72, 102, 108, 136, 144, 153, 204, 216, 272, 306, 408, 432, 459, 612, 816, 918, 1224, 1836, 2448, 3672, 7344 respectively. There are 3 commonly used methods to find the HCF of 1260 and 7344 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 1260 and 7344
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 1260 and 7344?

Answer: HCF of 1260 and 7344 is 36.

Explanation:

The HCF of two non-zero integers, x(1260) and y(7344), is the highest positive integer m(36) that divides both x(1260) and y(7344) without any remainder.

Methods to Find HCF of 1260 and 7344

Let's look at the different methods for finding the HCF of 1260 and 7344.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 1260 and 7344 by Prime Factorization

Prime factorization of 1260 and 7344 is (2 × 2 × 3 × 3 × 5 × 7) and (2 × 2 × 2 × 2 × 3 × 3 × 3 × 17) respectively. As visible, 1260 and 7344 have common prime factors. Hence, the HCF of 1260 and 7344 is 2 × 2 × 3 × 3 = 36.

HCF of 1260 and 7344 by Listing Common Factors

Factors of 1260: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260
Factors of 7344: 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 34, 36, 48, 51, 54, 68, 72, 102, 108, 136, 144, 153, 204, 216, 272, 306, 408, 432, 459, 612, 816, 918, 1224, 1836, 2448, 3672, 7344

There are 9 common factors of 1260 and 7344, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 1260 and 7344 is 36.

HCF of 1260 and 7344 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 = 7344 and Y = 1260

HCF(7344, 1260) = HCF(1260, 7344 mod 1260) = HCF(1260, 1044)
HCF(1260, 1044) = HCF(1044, 1260 mod 1044) = HCF(1044, 216)
HCF(1044, 216) = HCF(216, 1044 mod 216) = HCF(216, 180)
HCF(216, 180) = HCF(180, 216 mod 180) = HCF(180, 36)
HCF(180, 36) = HCF(36, 180 mod 36) = HCF(36, 0)
HCF(36, 0) = 36 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1260 and 7344 is 36.

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HCF of 1260 and 7344 Examples

Example 1: Find the HCF of 1260 and 7344, if their LCM is 257040.

Solution:

∵ LCM × HCF = 1260 × 7344
⇒ HCF(1260, 7344) = (1260 × 7344)/257040 = 36
Therefore, the highest common factor of 1260 and 7344 is 36.
Example 2: For two numbers, HCF = 36 and LCM = 257040. If one number is 1260, find the other number.

Solution:

Given: HCF (x, 1260) = 36 and LCM (x, 1260) = 257040
∵ HCF × LCM = 1260 × (x)
⇒ x = (HCF × LCM)/1260
⇒ x = (36 × 257040)/1260
⇒ x = 7344
Therefore, the other number is 7344.
Example 3: Find the highest number that divides 1260 and 7344 exactly.

Solution:

The highest number that divides 1260 and 7344 exactly is their highest common factor, i.e. HCF of 1260 and 7344.
⇒ Factors of 1260 and 7344:
- Factors of 1260 = 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260
- Factors of 7344 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 34, 36, 48, 51, 54, 68, 72, 102, 108, 136, 144, 153, 204, 216, 272, 306, 408, 432, 459, 612, 816, 918, 1224, 1836, 2448, 3672, 7344
Therefore, the HCF of 1260 and 7344 is 36.

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FAQs on HCF of 1260 and 7344

What is the HCF of 1260 and 7344?

The HCF of 1260 and 7344 is 36. To calculate the HCF (Highest Common Factor) of 1260 and 7344, we need to factor each number (factors of 1260 = 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260; factors of 7344 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 34, 36, 48, 51, 54, 68, 72, 102, 108, 136, 144, 153, 204, 216, 272, 306, 408, 432, 459, 612, 816, 918, 1224, 1836, 2448, 3672, 7344) and choose the highest factor that exactly divides both 1260 and 7344, i.e., 36.

If the HCF of 7344 and 1260 is 36, Find its LCM.

HCF(7344, 1260) × LCM(7344, 1260) = 7344 × 1260
Since the HCF of 7344 and 1260 = 36
⇒ 36 × LCM(7344, 1260) = 9253440
Therefore, LCM = 257040
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 1260, 7344?

The following equation can be used to express the relation between LCM and HCF of 1260 and 7344, i.e. HCF × LCM = 1260 × 7344.

How to Find the HCF of 1260 and 7344 by Long Division Method?

To find the HCF of 1260, 7344 using long division method, 7344 is divided by 1260. The corresponding divisor (36) when remainder equals 0 is taken as HCF.

How to Find the HCF of 1260 and 7344 by Prime Factorization?

To find the HCF of 1260 and 7344, we will find the prime factorization of the given numbers, i.e. 1260 = 2 × 2 × 3 × 3 × 5 × 7; 7344 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 17.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 1260 and 7344. Hence, HCF(1260, 7344) = 2 × 2 × 3 × 3 = 36
☛ What are Prime Numbers?

What are the Methods to Find HCF of 1260 and 7344?

There are three commonly used methods to find the HCF of 1260 and 7344.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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