The HCF of 34 and 85 is 17. The largest positive integer that divides both 34 and 85 evenly is the Highest Common Factor (HCF) of 34 and 85. Students are recommended to learn the HCF concept thoroughly right from the beginning as it is considered a vital concept in Mathematics. Those who are in search of the best material to learn the Highest Common Factor can rely on the article Highest Common Factor prepared by expert faculty in a simple and lucid manner. Learn the simple technique of how to calculate the Highest Common Factor of 34 and 85 with the help of solved examples and FAQs in this article.
What is the HCF of 34 and 85?
The Highest Common Factor of 34 and 85 is 17. The factors of 34 and 85 are 1, 2, 17, 34 and 1, 5, 17 and 85, respectively. Clearly, the largest number present in the factors of both 34 and 85 is 17. Therefore, 17 is the Highest Common Factor of 34 and 85.
How to Find HCF of 34 and 85?
The methods given below are used to find the HCF of 34 and 85:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 34 and 85 by Prime Factorisation Method
In the prime factorisation, to determine the HCF, write the given numbers as the product of prime factors. Hence, 34 and 85 can be written as:
34 = 2 × 17
85 = 5 × 17
The only common prime factor of 34 and 85 is 17.
Therefore, HCF (34, 85) = 17
HCF of 34 and 85 by Long Division Method
Follow the steps given below to determine the HCF of 34 and 85 by using the long division method:
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not 0, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Repeat this process until we get the remainder as zero. The last divisor will be the HCF of the given two numbers.
For 34 and 85, the HCF by long division method is given below:
Therefore, HCF (34, 85) = 17
HCF of 34 and 85 by Listing Common Factors
In this method, we find the HCF of 34 and 85 by listing out the common factors of 34 and 85. The factors of 34 and 85 are mentioned below:
Factors of 34:1, 2, 17, 34
Factors of 85: 1, 5, 17, 85
Therefore, HCF (34, 85) = 17
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Solved Example
Question: What is the HCF of 34 and 85 if their LCM is 170?
Solution: Given
LCM = 170
We know that
LCM × HCF = 34 × 85
170 × HCF = 34 × 85
HCF = 2890/170 = 17
Hence, the Highest Common Factor of 34 and 85 is 17.
Frequently Asked Questions on HCF of 34 and 85
What is the HCF of 34 and 85?
Is the HCF of 34 and 85 the same as the HCF of 17 and 34?
27 is the HCF of 34 and 85. True or False.
Name the methods to find the HCF of 34 and 85.
The following methods are used to find the HCF of 34 and 85
Prime Factorisation
Long Division method
Listing common factors
Calculate the HCF of 34 and 85 by using the prime factorisation method.
In the prime factorisation method, we express the numbers as the product of prime factors
34 = 2 × 17
85 = 5 × 17
Common prime factor of 34 and 85 is 17
Therefore, HCF (34, 85) = 17
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