The HCF of 100 and 190 is 10. The greatest number that divides 100 and 190 exactly and without a remainder is the HCF of these numbers. 1, 2, 4, 5, 10, 20, 25, 50, 100, and 1, 2, 5, 10, 19, 38, 95, 190, are factors of 100 and 190, respectively. The three most popular approaches for determining the HCF of 100 and 190 are listing common factors, prime factorisation, and long division.
Also read: Highest common factor
What is the HCF of 100 and 190?
The answer to this question is 10. This article shows the HCF of 100 and 190 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.
How to Find HCF of 100 and 190?
There are three methods to find the HCF of 100 and 190:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 100 and 190 by Prime Factorisation Method
The prime factorisation of 100 and 190 is given by:
Prime factorisation of 100 = (2 × 2 × 5 × 5)
Prime factorisation of 190 = (2 × 5 × 19)
Hence, the HCF of 100 and 190 is 2 × 5 = 10.
HCF (100, 190) = 10
HCF of 100 and 190 by Long Division Method
The divisor that we receive when the remainder becomes 0 after doing long division repeatedly is HCF of 100 and 190.
No further division can be done.
Hence, HCF (100, 190) = 10
HCF of 100 and 190 by Listing Common Factors
To calculate the HCF of 100 and 190 by listing common factors, list the factors as shown below:
Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 190 = 1, 2, 5, 10, 19, 38, 95, 190
There are 4 common factors of 100 and 190, and they are 1, 2, 5, and 10. Therefore, the Highest Common Factor of 100 and 190 is 10.
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Video Lesson on Properties of HCF and LCM
HCF of 100 and 190 Solved Example
For two numbers, HCF = 10 and LCM = 1900. If one number is 190, find the other number.
Solution:
Given: HCF (x, 190) = 10 and LCM (x, 190) = 1900
We know that HCF × LCM = 190 × (x)
⇒ x = (HCF × LCM)/190
⇒ x = (10 × 1900)/190
⇒ x = 100
Therefore, the other number is 100.
Frequently Asked Questions on HCF of 100 and 190
What is the HCF of 100 and 190?
How to find the HCF of 100 and 190 by prime factorisation?
⇒ 2 and 5 are common factors in the prime factorisation of 100 and 190. Hence, HCF (100, 190) = 2 × 5 = 10
What are the methods to find HCF of 100 and 190?
Long Division
Listing Common Factors
Prime Factorisation
What is the relation between LCM and HCF of 100, 190?
If the HCF of 190 and 100 is 10, find their LCM.
Since the HCF of 190 and 100 = 10
⇒ 10 × LCM (190, 100) = 19000
Therefore, LCM = 1900
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