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HCF of 240 and 6552

HCF of 240 and 6552 is the largest possible number that divides 240 and 6552 exactly without any remainder. The factors of 240 and 6552 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 and 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 28, 36, 39, 42, 52, 56, 63, 72, 78, 84, 91, 104, 117, 126, 156, 168, 182, 234, 252, 273, 312, 364, 468, 504, 546, 728, 819, 936, 1092, 1638, 2184, 3276, 6552 respectively. There are 3 commonly used methods to find the HCF of 240 and 6552 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 240 and 6552
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 240 and 6552?

Answer: HCF of 240 and 6552 is 24.

Explanation:

The HCF of two non-zero integers, x(240) and y(6552), is the highest positive integer m(24) that divides both x(240) and y(6552) without any remainder.

Methods to Find HCF of 240 and 6552

The methods to find the HCF of 240 and 6552 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 240 and 6552 by Prime Factorization

Prime factorization of 240 and 6552 is (2 × 2 × 2 × 2 × 3 × 5) and (2 × 2 × 2 × 3 × 3 × 7 × 13) respectively. As visible, 240 and 6552 have common prime factors. Hence, the HCF of 240 and 6552 is 2 × 2 × 2 × 3 = 24.

HCF of 240 and 6552 by Long Division

HCF of 240 and 6552 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 6552 (larger number) by 240 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (240) by the remainder (72).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the HCF of 240 and 6552.

HCF of 240 and 6552 by Listing Common Factors

Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
Factors of 6552: 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 28, 36, 39, 42, 52, 56, 63, 72, 78, 84, 91, 104, 117, 126, 156, 168, 182, 234, 252, 273, 312, 364, 468, 504, 546, 728, 819, 936, 1092, 1638, 2184, 3276, 6552

There are 8 common factors of 240 and 6552, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the highest common factor of 240 and 6552 is 24.

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HCF of 240 and 6552 Examples

Example 1: Find the HCF of 240 and 6552, if their LCM is 65520.

Solution:

∵ LCM × HCF = 240 × 6552
⇒ HCF(240, 6552) = (240 × 6552)/65520 = 24
Therefore, the highest common factor of 240 and 6552 is 24.
Example 2: Find the highest number that divides 240 and 6552 exactly.

Solution:

The highest number that divides 240 and 6552 exactly is their highest common factor, i.e. HCF of 240 and 6552.
⇒ Factors of 240 and 6552:
- Factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
- Factors of 6552 = 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 28, 36, 39, 42, 52, 56, 63, 72, 78, 84, 91, 104, 117, 126, 156, 168, 182, 234, 252, 273, 312, 364, 468, 504, 546, 728, 819, 936, 1092, 1638, 2184, 3276, 6552
Therefore, the HCF of 240 and 6552 is 24.
Example 3: The product of two numbers is 1572480. If their HCF is 24, what is their LCM?

Solution:

Given: HCF = 24 and product of numbers = 1572480
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1572480/24
Therefore, the LCM is 65520.

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FAQs on HCF of 240 and 6552

What is the HCF of 240 and 6552?

The HCF of 240 and 6552 is 24. To calculate the HCF (Highest Common Factor) of 240 and 6552, we need to factor each number (factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240; factors of 6552 = 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 28, 36, 39, 42, 52, 56, 63, 72, 78, 84, 91, 104, 117, 126, 156, 168, 182, 234, 252, 273, 312, 364, 468, 504, 546, 728, 819, 936, 1092, 1638, 2184, 3276, 6552) and choose the highest factor that exactly divides both 240 and 6552, i.e., 24.

How to Find the HCF of 240 and 6552 by Long Division Method?

To find the HCF of 240, 6552 using long division method, 6552 is divided by 240. The corresponding divisor (24) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 240 and 6552?

There are three commonly used methods to find the HCF of 240 and 6552.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the HCF of 6552 and 240 is 24, Find its LCM.

HCF(6552, 240) × LCM(6552, 240) = 6552 × 240
Since the HCF of 6552 and 240 = 24
⇒ 24 × LCM(6552, 240) = 1572480
Therefore, LCM = 65520
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What is the Relation Between LCM and HCF of 240, 6552?

The following equation can be used to express the relation between Least Common Multiple and HCF of 240 and 6552, i.e. HCF × LCM = 240 × 6552.

How to Find the HCF of 240 and 6552 by Prime Factorization?

To find the HCF of 240 and 6552, we will find the prime factorization of the given numbers, i.e. 240 = 2 × 2 × 2 × 2 × 3 × 5; 6552 = 2 × 2 × 2 × 3 × 3 × 7 × 13.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 240 and 6552. Hence, HCF(240, 6552) = 2 × 2 × 2 × 3 = 24
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