HCF of 16 and 64

HCF of 16 and 64 is the largest possible number that divides 16 and 64 exactly without any remainder. The factors of 16 and 64 are 1, 2, 4, 8, 16 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the HCF of 16 and 64 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 16 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 64?

Answer: HCF of 16 and 64 is 16.

Explanation:

The HCF of two non-zero integers, x(16) and y(64), is the highest positive integer m(16) that divides both x(16) and y(64) without any remainder.

Methods to Find HCF of 16 and 64

The methods to find the HCF of 16 and 64 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 16 and 64 by Long Division

HCF of 16 and 64 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 64 (larger number) by 16 (smaller number).
Step 2: Since the remainder = 0, the divisor (16) is the HCF of 16 and 64.

The corresponding divisor (16) is the HCF of 16 and 64.

HCF of 16 and 64 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 5 common factors of 16 and 64, that are 1, 2, 4, 8, and 16. Therefore, the highest common factor of 16 and 64 is 16.

HCF of 16 and 64 by Prime Factorization

Prime factorization of 16 and 64 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 16 and 64 have common prime factors. Hence, the HCF of 16 and 64 is 2 × 2 × 2 × 2 = 16.

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HCF of 16 and 64 Examples

Example 1: Find the HCF of 16 and 64, if their LCM is 64.

Solution:

∵ LCM × HCF = 16 × 64
⇒ HCF(16, 64) = (16 × 64)/64 = 16
Therefore, the highest common factor of 16 and 64 is 16.
Example 2: For two numbers, HCF = 16 and LCM = 64. If one number is 64, find the other number.

Solution:

Given: HCF (z, 64) = 16 and LCM (z, 64) = 64
∵ HCF × LCM = 64 × (z)
⇒ z = (HCF × LCM)/64
⇒ z = (16 × 64)/64
⇒ z = 16
Therefore, the other number is 16.
Example 3: The product of two numbers is 1024. If their HCF is 16, what is their LCM?

Solution:

Given: HCF = 16 and product of numbers = 1024
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1024/16
Therefore, the LCM is 64.

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FAQs on HCF of 16 and 64

What is the HCF of 16 and 64?

The HCF of 16 and 64 is 16. To calculate the Highest common factor of 16 and 64, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the highest factor that exactly divides both 16 and 64, i.e., 16.

How to Find the HCF of 16 and 64 by Prime Factorization?

To find the HCF of 16 and 64, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 64. Hence, HCF(16, 64) = 2 × 2 × 2 × 2 = 16
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How to Find the HCF of 16 and 64 by Long Division Method?

To find the HCF of 16, 64 using long division method, 64 is divided by 16. The corresponding divisor (16) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 16 and 64?

There are three commonly used methods to find the HCF of 16 and 64.

By Listing Common Factors
By Prime Factorization
By Long Division

If the HCF of 64 and 16 is 16, Find its LCM.

HCF(64, 16) × LCM(64, 16) = 64 × 16
Since the HCF of 64 and 16 = 16
⇒ 16 × LCM(64, 16) = 1024
Therefore, LCM = 64
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What is the Relation Between LCM and HCF of 16, 64?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 16 and 64, i.e. HCF × LCM = 16 × 64.

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