The HCF of 34 and 102 is 34. The highest integer, which divides the two given numbers exactly, is the HCF value. The factors of 34 are 1, 2, 17, 34, and the factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. Find the HCF value using the methods of prime factorisation, long division and listing common factors, explained in this article by the subject experts at BYJU’S.
What is the HCF of 34 and 102?
The answer to this question is 34. You will learn how to find the HCF of 34 and 102 using various methods in this article. The HCF of 34 and 102 is 34, which divides both 34 and 102 exactly.
Also read: Highest common factor
How to Find HCF of 34 and 102?
There are three methods to find the HCF of 34 and 102
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 34 and 102 by Prime Factorisation Method
The prime factorisation of 34 and 102 is given by:
34 = 2 × 17
102 = 2 × 3 × 17
Common prime factors of 34 and 102 = 2, 17
Therefore, HCF (34, 102) = 2 × 17 = 34
HCF of 34 and 102 by Long Division Method
To find the HCF, the numbers (34, 102) have to be divided by the prime factors. The HCF of 34 and 102 is the divisor we get when the remainder is zero after repeated long division.
No further division can be done.
Hence, HCF (34, 102) = 34
HCF of 34 and 102 by Listing Common Factors
To find the HCF of 34 and 102, the common factors have to be listed as given below:
Factors of 34: 1, 2, 17, 34
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
There are 4 common factors of 34 and 102, and they are 1, 2, 17 and 34.
Therefore, the highest common factor of 34 and 102 is 34.
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Video Lesson on Properties of HCF and LCM
HCF of 34 and 102 Solved Example
Question: If the product of two numbers = 3468 and HCF = 34, find the LCM.
Solution:
Given
Product of two numbers = 3468
HCF = 34
HCF × LCM = Product of two numbers
34 × LCM = 3468
LCM = 3468/34
LCM = 102
Hence, the LCM is 102.
Frequently Asked Questions on HCF of 34 and 102
What is the HCF of 34 and 102 if the LCM is 102?
Given
LCM = 102
LCM × HCF = 34 × 102
HCF = (34 × 102)/ 102
HCF = 34
How can we find the HCF of 34 and 102 using the long division method?
Write the methods used to calculate the HCF of 34 and 102.
What is the HCF of 34 and 102?
Write the relation between HCF and LCM of 34 and 102.
The relation between HCF and LCM of 34 and 102 is
HCF × LCM = 34 × 102
HCF × LCM = 3468
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