The HCF of 105 and 154 is 7. The numbers 105 and 154 are divisible evenly by the HCF value. The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105,and the factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154. Get a good hold on the HCF concepts and methods like prime factorisation, long division and listing common factors in this article for absolutely free of cost.
Also read: Highest common factor
What is the HCF 105 and 154?
The answer to this question is 7. The different methods used in finding the HCF of 105 and 154 are provided in this article. The HCF of 105 and 154 is 7, which divides the given two numbers exactly.
How to Find HCF of 105 and 154?
The methods used to find the HCF of 105 and 154 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 105 and 154 by Prime Factorisation Method
The prime factorisation of 105 and 154 is given by:
105 = 3 × 5 × 7
154 = 2 × 7 × 11
Common factors = 7
HCF (105, 154) = 7
HCF of 105 and 154 by Long Division Method
The numbers (105, 154), when divided by the prime factors, help in finding the HCF of 105 and 154. After repeated long division, the divisor with zero as the remainder is the HCF.
No further division can be done.
Hence, HCF (105, 154) = 7
HCF of 105 and 154 by Listing Common Factors
You can find the HCF of 105 and 154 by listing common factors as shown below.
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 154: 1, 2, 7, 11, 14, 22, 77, 154
There are 2 common factors of 105 and 154, and they are 1 and 7.
Therefore, the highest common factor of 105 and 154 is 7.
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- Prime Factorisation
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Video Lesson on Properties of HCF and LCM
HCF of 105 and 154 Solved Example
Question: What is the HCF of 105 and 154 if the LCM is 2310?
Solution:
Given,
LCM = 2310
We know that;
HCF × LCM = 105 × 154
HCF = (105 × 154)/2310
HCF = 7
Hence, the HCF is 7.
Frequently Asked Questions on HCF of 105 and 154
What is the HCF of 105 and 154?
Using the long division, find the HCF of 105 and 154.
List the methods to find HCF of 105 and 154.
If LCM = 2310 and HCF = 7 for two numbers, find the other number when one number is 105.
Consider y as the other number.
Given LCM = 2310 and HCF = 7
HCF × LCM = 105 × y
y = (HCF × LCM)/ 105
y = (7 × 2310)/ 105
y = 154
Therefore, the other number is 154.
Show the relation between HCF and LCM of 105 and 154.
The relation between HCF and LCM of 105 and 154 is
HCF × LCM = 105 × 154
HCF × LCM = 16170
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