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HCF of 56, 96 and 404

HCF of 56, 96 and 404 is the largest possible number that divides 56, 96 and 404 exactly without any remainder. The factors of 56, 96 and 404 are (1, 2, 4, 7, 8, 14, 28, 56), (1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and (1, 2, 4, 101, 202, 404) respectively. There are 3 commonly used methods to find the HCF of 56, 96 and 404 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 56, 96 and 404
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 56, 96 and 404?

Answer: HCF of 56, 96 and 404 is 4.

Explanation:

The HCF of three non-zero integers, x(56), y(96) and z(404), is the highest positive integer m(4) that divides x(56), y(96) and z(404) without any remainder.

Methods to Find HCF of 56, 96 and 404

Let's look at the different methods for finding the HCF of 56, 96 and 404.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 56, 96 and 404 by Listing Common Factors

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 404: 1, 2, 4, 101, 202, 404

There are 3 common factors of 56, 96 and 404, that are 1, 2, and 4. Therefore, the highest common factor of 56, 96 and 404 is 4.

HCF of 56, 96 and 404 by Long Division

HCF of 56, 96 and 404 can be represented as HCF of (HCF of 56, 96) and 404. HCF(56, 96, 404) can be thus calculated by first finding HCF(56, 96) using long division and thereafter using this result with 404 to perform long division again.

Step 1: Divide 96 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (40). Repeat this process until the remainder = 0.
⇒ HCF(56, 96) = 8.
Step 3: Now to find the HCF of 8 and 404, we will perform a long division on 404 and 8.
Step 4: For remainder = 0, divisor = 4 ⇒ HCF(8, 404) = 4

Thus, HCF(56, 96, 404) = HCF(HCF(56, 96), 404) = 4.

HCF of 56, 96 and 404 by Prime Factorization

Prime factorization of 56, 96 and 404 is (2 × 2 × 2 × 7), (2 × 2 × 2 × 2 × 2 × 3) and (2 × 2 × 101) respectively. As visible, 56, 96 and 404 have common prime factors. Hence, the HCF of 56, 96 and 404 is 2 × 2 = 4.

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HCF of 56, 96 and 404 Examples

Example 1: Calculate the HCF of 56, 96, and 404 using LCM of the given numbers.

Solution:

Prime factorization of 56, 96 and 404 is given as,
- 56 = 2 × 2 × 2 × 7
- 96 = 2 × 2 × 2 × 2 × 2 × 3
- 404 = 2 × 2 × 101
LCM(56, 96) = 672, LCM(96, 404) = 9696, LCM(404, 56) = 5656, LCM(56, 96, 404) = 67872
⇒ HCF(56, 96, 404) = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(404, 56)]
⇒ HCF(56, 96, 404) = (2171904 × 67872)/(672 × 9696 × 5656)
⇒ HCF(56, 96, 404) = 4.
Therefore, the HCF of 56, 96 and 404 is 4.
Example 2: Verify the relation between the LCM and HCF of 56, 96 and 404.

Solution:

The relation between the LCM and HCF of 56, 96 and 404 is given as, HCF(56, 96, 404) = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(56, 404)]
⇒ Prime factorization of 56, 96 and 404:
- 56 = 2 × 2 × 2 × 7
- 96 = 2 × 2 × 2 × 2 × 2 × 3
- 404 = 2 × 2 × 101
∴ LCM of (56, 96), (96, 404), (56, 404), and (56, 96, 404) is 672, 9696, 5656, and 67872 respectively.
Now, LHS = HCF(56, 96, 404) = 4.
And, RHS = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(56, 404)] = [(2171904) × 67872]/[672 × 9696 × 5656]
LHS = RHS = 4.
Hence verified.
Example 3: Find the highest number that divides 56, 96, and 404 completely.

Solution:

The highest number that divides 56, 96, and 404 exactly is their highest common factor.
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 404 = 1, 2, 4, 101, 202, 404
The HCF of 56, 96, and 404 is 4.
∴ The highest number that divides 56, 96, and 404 is 4.

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FAQs on HCF of 56, 96 and 404

What is the HCF of 56, 96 and 404?

The HCF of 56, 96 and 404 is 4. To calculate the highest common factor of 56, 96 and 404, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96; factors of 404 = 1, 2, 4, 101, 202, 404) and choose the highest factor that exactly divides 56, 96 and 404, i.e., 4.

How to Find the HCF of 56, 96 and 404 by Prime Factorization?

To find the HCF of 56, 96 and 404, we will find the prime factorization of given numbers, i.e. 56 = 2 × 2 × 2 × 7; 96 = 2 × 2 × 2 × 2 × 2 × 3; 404 = 2 × 2 × 101.
⇒ Since 2, 2 are common terms in the prime factorization of 56, 96 and 404. Hence, HCF(56, 96, 404) = 2 × 2 = 4
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What is the Relation Between LCM and HCF of 56, 96 and 404?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 56, 96 and 404, i.e. HCF(56, 96, 404) = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(56, 404)].
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What are the Methods to Find HCF of 56, 96 and 404?

There are three commonly used methods to find the HCF of 56, 96 and 404.

By Prime Factorization
By Euclidean Algorithm
By Long Division

Which of the following is HCF of 56, 96 and 404? 4, 421, 426, 437, 412, 421

HCF of 56, 96, 404 will be the number that divides 56, 96, and 404 without leaving any remainder. The only number that satisfies the given condition is 4.

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