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HCF of 16 and 44

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

1.	HCF of 16 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 44?

Answer: HCF of 16 and 44 is 4.

Explanation:

The HCF of two non-zero integers, x(16) and y(44), is the highest positive integer m(4) that divides both x(16) and y(44) without any remainder.

Methods to Find HCF of 16 and 44

The methods to find the HCF of 16 and 44 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 16 and 44 by Prime Factorization

Prime factorization of 16 and 44 is (2 × 2 × 2 × 2) and (2 × 2 × 11) respectively. As visible, 16 and 44 have common prime factors. Hence, the HCF of 16 and 44 is 2 × 2 = 4.

HCF of 16 and 44 by Long Division

HCF of 16 and 44 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 44 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 16 and 44.

HCF of 16 and 44 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 44: 1, 2, 4, 11, 22, 44

There are 3 common factors of 16 and 44, that are 1, 2, and 4. Therefore, the highest common factor of 16 and 44 is 4.

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HCF of 16 and 44 Examples

Example 1: Find the highest number that divides 16 and 44 exactly.

Solution:

The highest number that divides 16 and 44 exactly is their highest common factor, i.e. HCF of 16 and 44.
⇒ Factors of 16 and 44:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the HCF of 16 and 44 is 4.
Example 2: Find the HCF of 16 and 44, if their LCM is 176.

Solution:

∵ LCM × HCF = 16 × 44
⇒ HCF(16, 44) = (16 × 44)/176 = 4
Therefore, the highest common factor of 16 and 44 is 4.
Example 3: For two numbers, HCF = 4 and LCM = 176. If one number is 44, find the other number.

Solution:

Given: HCF (x, 44) = 4 and LCM (x, 44) = 176
∵ HCF × LCM = 44 × (x)
⇒ x = (HCF × LCM)/44
⇒ x = (4 × 176)/44
⇒ x = 16
Therefore, the other number is 16.

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FAQs on HCF of 16 and 44

What is the HCF of 16 and 44?

The HCF of 16 and 44 is 4. To calculate the Highest common factor (HCF) of 16 and 44, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the highest factor that exactly divides both 16 and 44, i.e., 4.

If the HCF of 44 and 16 is 4, Find its LCM.

HCF(44, 16) × LCM(44, 16) = 44 × 16
Since the HCF of 44 and 16 = 4
⇒ 4 × LCM(44, 16) = 704
Therefore, LCM = 176
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How to Find the HCF of 16 and 44 by Long Division Method?

To find the HCF of 16, 44 using long division method, 44 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 16 and 44 by Prime Factorization?

To find the HCF of 16 and 44, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 44 = 2 × 2 × 11.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 44. Hence, HCF(16, 44) = 2 × 2 = 4
☛ What is a Prime Number?

What is the Relation Between LCM and HCF of 16, 44?

The following equation can be used to express the relation between LCM and HCF of 16 and 44, i.e. HCF × LCM = 16 × 44.

What are the Methods to Find HCF of 16 and 44?

There are three commonly used methods to find the HCF of 16 and 44.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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