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HCF of 408 and 1032

HCF of 408 and 1032 is the largest possible number that divides 408 and 1032 exactly without any remainder. The factors of 408 and 1032 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408 and 1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032 respectively. There are 3 commonly used methods to find the HCF of 408 and 1032 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 408 and 1032
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 408 and 1032?

Answer: HCF of 408 and 1032 is 24.

Explanation:

The HCF of two non-zero integers, x(408) and y(1032), is the highest positive integer m(24) that divides both x(408) and y(1032) without any remainder.

Methods to Find HCF of 408 and 1032

Let's look at the different methods for finding the HCF of 408 and 1032.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 408 and 1032 by Long Division

HCF of 408 and 1032 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1032 (larger number) by 408 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (408) by the remainder (216).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the HCF of 408 and 1032.

HCF of 408 and 1032 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 = 1032 and Y = 408

HCF(1032, 408) = HCF(408, 1032 mod 408) = HCF(408, 216)
HCF(408, 216) = HCF(216, 408 mod 216) = HCF(216, 192)
HCF(216, 192) = HCF(192, 216 mod 192) = HCF(192, 24)
HCF(192, 24) = HCF(24, 192 mod 24) = HCF(24, 0)
HCF(24, 0) = 24 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 408 and 1032 is 24.

HCF of 408 and 1032 by Prime Factorization

Prime factorization of 408 and 1032 is (2 × 2 × 2 × 3 × 17) and (2 × 2 × 2 × 3 × 43) respectively. As visible, 408 and 1032 have common prime factors. Hence, the HCF of 408 and 1032 is 2 × 2 × 2 × 3 = 24.

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HCF of 408 and 1032 Examples

Example 1: For two numbers, HCF = 24 and LCM = 17544. If one number is 1032, find the other number.

Solution:

Given: HCF (x, 1032) = 24 and LCM (x, 1032) = 17544
∵ HCF × LCM = 1032 × (x)
⇒ x = (HCF × LCM)/1032
⇒ x = (24 × 17544)/1032
⇒ x = 408
Therefore, the other number is 408.
Example 2: The product of two numbers is 421056. If their HCF is 24, what is their LCM?

Solution:

Given: HCF = 24 and product of numbers = 421056
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 421056/24
Therefore, the LCM is 17544.
Example 3: Find the HCF of 408 and 1032, if their LCM is 17544.

Solution:

∵ LCM × HCF = 408 × 1032
⇒ HCF(408, 1032) = (408 × 1032)/17544 = 24
Therefore, the highest common factor of 408 and 1032 is 24.

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FAQs on HCF of 408 and 1032

What is the HCF of 408 and 1032?

The HCF of 408 and 1032 is 24. To calculate the HCF (Highest Common Factor) of 408 and 1032, we need to factor each number (factors of 408 = 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408; factors of 1032 = 1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032) and choose the highest factor that exactly divides both 408 and 1032, i.e., 24.

What is the Relation Between LCM and HCF of 408, 1032?

The following equation can be used to express the relation between Least Common Multiple and HCF of 408 and 1032, i.e. HCF × LCM = 408 × 1032.

If the HCF of 1032 and 408 is 24, Find its LCM.

HCF(1032, 408) × LCM(1032, 408) = 1032 × 408
Since the HCF of 1032 and 408 = 24
⇒ 24 × LCM(1032, 408) = 421056
Therefore, LCM = 17544
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How to Find the HCF of 408 and 1032 by Prime Factorization?

To find the HCF of 408 and 1032, we will find the prime factorization of the given numbers, i.e. 408 = 2 × 2 × 2 × 3 × 17; 1032 = 2 × 2 × 2 × 3 × 43.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 408 and 1032. Hence, HCF(408, 1032) = 2 × 2 × 2 × 3 = 24
☛ What is a Prime Number?

What are the Methods to Find HCF of 408 and 1032?

There are three commonly used methods to find the HCF of 408 and 1032.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 408 and 1032 by Long Division Method?

To find the HCF of 408, 1032 using long division method, 1032 is divided by 408. The corresponding divisor (24) when remainder equals 0 is taken as HCF.

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