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HCF of 616 and 32

HCF of 616 and 32 is the largest possible number that divides 616 and 32 exactly without any remainder. The factors of 616 and 32 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the HCF of 616 and 32 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 616 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 616 and 32?

Answer: HCF of 616 and 32 is 8.

Explanation:

The HCF of two non-zero integers, x(616) and y(32), is the highest positive integer m(8) that divides both x(616) and y(32) without any remainder.

Methods to Find HCF of 616 and 32

The methods to find the HCF of 616 and 32 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

HCF of 616 and 32 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 = 616 and Y = 32

HCF(616, 32) = HCF(32, 616 mod 32) = HCF(32, 8)
HCF(32, 8) = HCF(8, 32 mod 8) = HCF(8, 0)
HCF(8, 0) = 8 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 616 and 32 is 8.

HCF of 616 and 32 by Listing Common Factors

Factors of 616: 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
Factors of 32: 1, 2, 4, 8, 16, 32

There are 4 common factors of 616 and 32, that are 8, 1, 2, and 4. Therefore, the highest common factor of 616 and 32 is 8.

HCF of 616 and 32 by Prime Factorization

Prime factorization of 616 and 32 is (2 × 2 × 2 × 7 × 11) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 616 and 32 have common prime factors. Hence, the HCF of 616 and 32 is 2 × 2 × 2 = 8.

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HCF of 616 and 32 Examples

Example 1: Find the highest number that divides 616 and 32 exactly.

Solution:

The highest number that divides 616 and 32 exactly is their highest common factor, i.e. HCF of 616 and 32.
⇒ Factors of 616 and 32:
- Factors of 616 = 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the HCF of 616 and 32 is 8.
Example 2: For two numbers, HCF = 8 and LCM = 2464. If one number is 616, find the other number.

Solution:

Given: HCF (z, 616) = 8 and LCM (z, 616) = 2464
∵ HCF × LCM = 616 × (z)
⇒ z = (HCF × LCM)/616
⇒ z = (8 × 2464)/616
⇒ z = 32
Therefore, the other number is 32.
Example 3: The product of two numbers is 19712. If their HCF is 8, what is their LCM?

Solution:

Given: HCF = 8 and product of numbers = 19712
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 19712/8
Therefore, the LCM is 2464.

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FAQs on HCF of 616 and 32

What is the HCF of 616 and 32?

The HCF of 616 and 32 is 8. To calculate the Highest common factor of 616 and 32, we need to factor each number (factors of 616 = 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the highest factor that exactly divides both 616 and 32, i.e., 8.

What are the Methods to Find HCF of 616 and 32?

There are three commonly used methods to find the HCF of 616 and 32.

By Prime Factorization
By Long Division
By Listing Common Factors

If the HCF of 32 and 616 is 8, Find its LCM.

HCF(32, 616) × LCM(32, 616) = 32 × 616
Since the HCF of 32 and 616 = 8
⇒ 8 × LCM(32, 616) = 19712
Therefore, LCM = 2464
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How to Find the HCF of 616 and 32 by Prime Factorization?

To find the HCF of 616 and 32, we will find the prime factorization of the given numbers, i.e. 616 = 2 × 2 × 2 × 7 × 11; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 616 and 32. Hence, HCF(616, 32) = 2 × 2 × 2 = 8
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What is the Relation Between LCM and HCF of 616, 32?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 616 and 32, i.e. HCF × LCM = 616 × 32.

How to Find the HCF of 616 and 32 by Long Division Method?

To find the HCF of 616, 32 using long division method, 616 is divided by 32. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

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