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HCF of 2048 and 960

HCF of 2048 and 960 is the largest possible number that divides 2048 and 960 exactly without any remainder. The factors of 2048 and 960 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 respectively. There are 3 commonly used methods to find the HCF of 2048 and 960 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 2048 and 960
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 2048 and 960?

Answer: HCF of 2048 and 960 is 64.

Explanation:

The HCF of two non-zero integers, x(2048) and y(960), is the highest positive integer m(64) that divides both x(2048) and y(960) without any remainder.

Methods to Find HCF of 2048 and 960

Let's look at the different methods for finding the HCF of 2048 and 960.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 2048 and 960 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 = 2048 and Y = 960

HCF(2048, 960) = HCF(960, 2048 mod 960) = HCF(960, 128)
HCF(960, 128) = HCF(128, 960 mod 128) = HCF(128, 64)
HCF(128, 64) = HCF(64, 128 mod 64) = HCF(64, 0)
HCF(64, 0) = 64 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 2048 and 960 is 64.

HCF of 2048 and 960 by Prime Factorization

Prime factorization of 2048 and 960 is (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 2 × 2 × 3 × 5) respectively. As visible, 2048 and 960 have common prime factors. Hence, the HCF of 2048 and 960 is 2 × 2 × 2 × 2 × 2 × 2 = 64.

HCF of 2048 and 960 by Long Division

HCF of 2048 and 960 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 2048 (larger number) by 960 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (960) by the remainder (128).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (64) is the HCF of 2048 and 960.

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HCF of 2048 and 960 Examples

Example 1: For two numbers, HCF = 64 and LCM = 30720. If one number is 960, find the other number.

Solution:

Given: HCF (z, 960) = 64 and LCM (z, 960) = 30720
∵ HCF × LCM = 960 × (z)
⇒ z = (HCF × LCM)/960
⇒ z = (64 × 30720)/960
⇒ z = 2048
Therefore, the other number is 2048.
Example 2: The product of two numbers is 1966080. If their HCF is 64, what is their LCM?

Solution:

Given: HCF = 64 and product of numbers = 1966080
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1966080/64
Therefore, the LCM is 30720.
Example 3: Find the highest number that divides 2048 and 960 exactly.

Solution:

The highest number that divides 2048 and 960 exactly is their highest common factor, i.e. HCF of 2048 and 960.
⇒ Factors of 2048 and 960:
- Factors of 2048 = 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048
- Factors of 960 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
Therefore, the HCF of 2048 and 960 is 64.

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FAQs on HCF of 2048 and 960

What is the HCF of 2048 and 960?

The HCF of 2048 and 960 is 64. To calculate the HCF of 2048 and 960, we need to factor each number (factors of 2048 = 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048; factors of 960 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960) and choose the highest factor that exactly divides both 2048 and 960, i.e., 64.

How to Find the HCF of 2048 and 960 by Prime Factorization?

To find the HCF of 2048 and 960, we will find the prime factorization of the given numbers, i.e. 2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2; 960 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 2, 2, 2 are common terms in the prime factorization of 2048 and 960. Hence, HCF(2048, 960) = 2 × 2 × 2 × 2 × 2 × 2 = 64
☛ What is a Prime Number?

How to Find the HCF of 2048 and 960 by Long Division Method?

To find the HCF of 2048, 960 using long division method, 2048 is divided by 960. The corresponding divisor (64) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 2048, 960?

The following equation can be used to express the relation between Least Common Multiple and HCF of 2048 and 960, i.e. HCF × LCM = 2048 × 960.

If the HCF of 960 and 2048 is 64, Find its LCM.

HCF(960, 2048) × LCM(960, 2048) = 960 × 2048
Since the HCF of 960 and 2048 = 64
⇒ 64 × LCM(960, 2048) = 1966080
Therefore, LCM = 30720
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What are the Methods to Find HCF of 2048 and 960?

There are three commonly used methods to find the HCF of 2048 and 960.

By Long Division
By Prime Factorization
By Listing Common Factors

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