HCF of 16 and 100

HCF of 16 and 100 is the largest possible number that divides 16 and 100 exactly without any remainder. The factors of 16 and 100 are 1, 2, 4, 8, 16 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the HCF of 16 and 100 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 16 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 100?

Answer: HCF of 16 and 100 is 4.

Explanation:

The HCF of two non-zero integers, x(16) and y(100), is the highest positive integer m(4) that divides both x(16) and y(100) without any remainder.

Methods to Find HCF of 16 and 100

The methods to find the HCF of 16 and 100 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 16 and 100 by Long Division

HCF of 16 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 16 and 100.

HCF of 16 and 100 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 16 and 100, that are 1, 2, and 4. Therefore, the highest common factor of 16 and 100 is 4.

HCF of 16 and 100 by Prime Factorization

Prime factorization of 16 and 100 is (2 × 2 × 2 × 2) and (2 × 2 × 5 × 5) respectively. As visible, 16 and 100 have common prime factors. Hence, the HCF of 16 and 100 is 2 × 2 = 4.

☛ Also Check:

HCF of 16 and 100 Examples

Example 1: Find the highest number that divides 16 and 100 exactly.

Solution:

The highest number that divides 16 and 100 exactly is their highest common factor, i.e. HCF of 16 and 100.
⇒ Factors of 16 and 100:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the HCF of 16 and 100 is 4.
Example 2: The product of two numbers is 1600. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 1600
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1600/4
Therefore, the LCM is 400.
Example 3: For two numbers, HCF = 4 and LCM = 400. If one number is 16, find the other number.

Solution:

Given: HCF (y, 16) = 4 and LCM (y, 16) = 400
∵ HCF × LCM = 16 × (y)
⇒ y = (HCF × LCM)/16
⇒ y = (4 × 400)/16
⇒ y = 100
Therefore, the other number is 100.

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FAQs on HCF of 16 and 100

What is the HCF of 16 and 100?

The HCF of 16 and 100 is 4. To calculate the HCF of 16 and 100, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the highest factor that exactly divides both 16 and 100, i.e., 4.

What are the Methods to Find HCF of 16 and 100?

There are three commonly used methods to find the HCF of 16 and 100.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the HCF of 16 and 100 by Prime Factorization?

To find the HCF of 16 and 100, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 100. Hence, HCF(16, 100) = 2 × 2 = 4
☛ Prime Numbers

If the HCF of 100 and 16 is 4, Find its LCM.

HCF(100, 16) × LCM(100, 16) = 100 × 16
Since the HCF of 100 and 16 = 4
⇒ 4 × LCM(100, 16) = 1600
Therefore, LCM = 400
☛ HCF Calculator

What is the Relation Between LCM and HCF of 16, 100?

The following equation can be used to express the relation between Least Common Multiple and HCF of 16 and 100, i.e. HCF × LCM = 16 × 100.

How to Find the HCF of 16 and 100 by Long Division Method?

To find the HCF of 16, 100 using long division method, 100 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

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