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HCF of 1651 and 2032

HCF of 1651 and 2032 is the largest possible number that divides 1651 and 2032 exactly without any remainder. The factors of 1651 and 2032 are 1, 13, 127, 1651 and 1, 2, 4, 8, 16, 127, 254, 508, 1016, 2032 respectively. There are 3 commonly used methods to find the HCF of 1651 and 2032 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 1651 and 2032
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 1651 and 2032?

Answer: HCF of 1651 and 2032 is 127.

Explanation:

The HCF of two non-zero integers, x(1651) and y(2032), is the highest positive integer m(127) that divides both x(1651) and y(2032) without any remainder.

Methods to Find HCF of 1651 and 2032

The methods to find the HCF of 1651 and 2032 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 1651 and 2032 by Long Division

HCF of 1651 and 2032 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 2032 (larger number) by 1651 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (1651) by the remainder (381).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (127) is the HCF of 1651 and 2032.

HCF of 1651 and 2032 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 = 2032 and Y = 1651

HCF(2032, 1651) = HCF(1651, 2032 mod 1651) = HCF(1651, 381)
HCF(1651, 381) = HCF(381, 1651 mod 381) = HCF(381, 127)
HCF(381, 127) = HCF(127, 381 mod 127) = HCF(127, 0)
HCF(127, 0) = 127 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1651 and 2032 is 127.

HCF of 1651 and 2032 by Listing Common Factors

Factors of 1651: 1, 13, 127, 1651
Factors of 2032: 1, 2, 4, 8, 16, 127, 254, 508, 1016, 2032

There are 2 common factors of 1651 and 2032, that are 1 and 127. Therefore, the highest common factor of 1651 and 2032 is 127.

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HCF of 1651 and 2032 Examples

Example 1: The product of two numbers is 3354832. If their HCF is 127, what is their LCM?

Solution:

Given: HCF = 127 and product of numbers = 3354832
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 3354832/127
Therefore, the LCM is 26416.
Example 2: Find the HCF of 1651 and 2032, if their LCM is 26416.

Solution:

∵ LCM × HCF = 1651 × 2032
⇒ HCF(1651, 2032) = (1651 × 2032)/26416 = 127
Therefore, the highest common factor of 1651 and 2032 is 127.
Example 3: For two numbers, HCF = 127 and LCM = 26416. If one number is 2032, find the other number.

Solution:

Given: HCF (z, 2032) = 127 and LCM (z, 2032) = 26416
∵ HCF × LCM = 2032 × (z)
⇒ z = (HCF × LCM)/2032
⇒ z = (127 × 26416)/2032
⇒ z = 1651
Therefore, the other number is 1651.

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FAQs on HCF of 1651 and 2032

What is the HCF of 1651 and 2032?

The HCF of 1651 and 2032 is 127. To calculate the Highest common factor of 1651 and 2032, we need to factor each number (factors of 1651 = 1, 13, 127, 1651; factors of 2032 = 1, 2, 4, 8, 16, 127, 254, 508, 1016, 2032) and choose the highest factor that exactly divides both 1651 and 2032, i.e., 127.

If the HCF of 2032 and 1651 is 127, Find its LCM.

HCF(2032, 1651) × LCM(2032, 1651) = 2032 × 1651
Since the HCF of 2032 and 1651 = 127
⇒ 127 × LCM(2032, 1651) = 3354832
Therefore, LCM = 26416
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What is the Relation Between LCM and HCF of 1651, 2032?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 1651 and 2032, i.e. HCF × LCM = 1651 × 2032.

What are the Methods to Find HCF of 1651 and 2032?

There are three commonly used methods to find the HCF of 1651 and 2032.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 1651 and 2032 by Prime Factorization?

To find the HCF of 1651 and 2032, we will find the prime factorization of the given numbers, i.e. 1651 = 13 × 127; 2032 = 2 × 2 × 2 × 2 × 127.
⇒ Since 127 is the only common prime factor of 1651 and 2032. Hence, HCF (1651, 2032) = 127.
☛ Prime Numbers

How to Find the HCF of 1651 and 2032 by Long Division Method?

To find the HCF of 1651, 2032 using long division method, 2032 is divided by 1651. The corresponding divisor (127) when remainder equals 0 is taken as HCF.

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