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HCF of 100 and 190

HCF of 100 and 190 is the largest possible number that divides 100 and 190 exactly without any remainder. The factors of 100 and 190 are 1, 2, 4, 5, 10, 20, 25, 50, 100 and 1, 2, 5, 10, 19, 38, 95, 190 respectively. There are 3 commonly used methods to find the HCF of 100 and 190 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 100 and 190
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 100 and 190?

Answer: HCF of 100 and 190 is 10.

Explanation:

The HCF of two non-zero integers, x(100) and y(190), is the highest positive integer m(10) that divides both x(100) and y(190) without any remainder.

Methods to Find HCF of 100 and 190

Let's look at the different methods for finding the HCF of 100 and 190.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 100 and 190 by Long Division

HCF of 100 and 190 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 190 (larger number) by 100 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (100) by the remainder (90).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the HCF of 100 and 190.

HCF of 100 and 190 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 = 190 and Y = 100

HCF(190, 100) = HCF(100, 190 mod 100) = HCF(100, 90)
HCF(100, 90) = HCF(90, 100 mod 90) = HCF(90, 10)
HCF(90, 10) = HCF(10, 90 mod 10) = HCF(10, 0)
HCF(10, 0) = 10 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 100 and 190 is 10.

HCF of 100 and 190 by Prime Factorization

Prime factorization of 100 and 190 is (2 × 2 × 5 × 5) and (2 × 5 × 19) respectively. As visible, 100 and 190 have common prime factors. Hence, the HCF of 100 and 190 is 2 × 5 = 10.

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HCF of 100 and 190 Examples

Example 1: Find the highest number that divides 100 and 190 exactly.

Solution:

The highest number that divides 100 and 190 exactly is their highest common factor, i.e. HCF of 100 and 190.
⇒ Factors of 100 and 190:
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 190 = 1, 2, 5, 10, 19, 38, 95, 190
Therefore, the HCF of 100 and 190 is 10.
Example 2: Find the HCF of 100 and 190, if their LCM is 1900.

Solution:

∵ LCM × HCF = 100 × 190
⇒ HCF(100, 190) = (100 × 190)/1900 = 10
Therefore, the highest common factor of 100 and 190 is 10.
Example 3: For two numbers, HCF = 10 and LCM = 1900. If one number is 190, find the other number.

Solution:

Given: HCF (z, 190) = 10 and LCM (z, 190) = 1900
∵ HCF × LCM = 190 × (z)
⇒ z = (HCF × LCM)/190
⇒ z = (10 × 1900)/190
⇒ z = 100
Therefore, the other number is 100.

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FAQs on HCF of 100 and 190

What is the HCF of 100 and 190?

The HCF of 100 and 190 is 10. To calculate the Highest common factor of 100 and 190, we need to factor each number (factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100; factors of 190 = 1, 2, 5, 10, 19, 38, 95, 190) and choose the highest factor that exactly divides both 100 and 190, i.e., 10.

How to Find the HCF of 100 and 190 by Prime Factorization?

To find the HCF of 100 and 190, we will find the prime factorization of the given numbers, i.e. 100 = 2 × 2 × 5 × 5; 190 = 2 × 5 × 19.
⇒ Since 2, 5 are common terms in the prime factorization of 100 and 190. Hence, HCF(100, 190) = 2 × 5 = 10
☛ What is a Prime Number?

What are the Methods to Find HCF of 100 and 190?

There are three commonly used methods to find the HCF of 100 and 190.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and HCF of 100, 190?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 100 and 190, i.e. HCF × LCM = 100 × 190.

How to Find the HCF of 100 and 190 by Long Division Method?

To find the HCF of 100, 190 using long division method, 190 is divided by 100. The corresponding divisor (10) when remainder equals 0 is taken as HCF.

If the HCF of 190 and 100 is 10, Find its LCM.

HCF(190, 100) × LCM(190, 100) = 190 × 100
Since the HCF of 190 and 100 = 10
⇒ 10 × LCM(190, 100) = 19000
Therefore, LCM = 1900
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