The HCF of 85 and 153 is 17. The Highest Common Factor (HCF) of two or more numbers is the largest number among all the common factors of the given numbers. The factors of 85 and 153 are 1, 5, 17, 85, and 1, 3, 9, 17, 51, 153, respectively. Among these factors, the largest number that divides both 85 and 153 is 17. Therefore, the Highest Common Factor of 85 and 153 is 17. The article HCF drafted by BYJU’S experts is the best reference material for students to learn the HCF concept in-depth. In this article, let us learn the simple techniques to find the Highest Common Factor of 85 and 153 using prime factorisation, long division method and listing common factors.
What is the HCF of 85 and 153?
The answer to this question is 17. The largest number that divides both 85 and 153 is 17. Hence, 17 is the Highest Common Factor (HCF) of 85 and 153.
How to Find HCF of 85 and 153?
There are three methods to find the HCF of 85 and 153:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 85 and 153 by Prime Factorisation Method
In the prime factorisation, we express the numbers as the product of prime factors. To find the Highest Common Factor, multiply all the common prime factors with the lowest degree (power).
85 = 5 × 17
153 = 3 × 3 × 17
The Common prime factor of 85 and 153 is 17.
Therefore,
HCF of (85, 153) = 17
HCF of 85 and 153 by Long Division Method
The following steps are used to find the Highest Common Factor of 85 and 153.
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 zero, 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.
The HCF of 85 and 153 by the long division method is:
HCF (85, 153) = 17
HCF of 85 and 153 by Listing Common Factors
Here, we can find the Highest Common Factor by listing all the factors of given numbers. The factors of 85 and 153 are as follows:
Factors of 85: 1, 5, 17, 85
Factors of 153: 1, 3, 9, 17, 51, 153
Hence, HCF (85, 153) = 17
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 85 and 153 exactly?
Solution: The largest number that divides both 85 and 153 is their Highest Common Factor (HCF). Here, 17 is the Highest Common Factor of 85 and 153. Thus, the highest number that divides both 85 and 153 is 17.
2. What is the HCF of 85 and 153 if their LCM is 765?
Solution: We know that
LCM × HCF = 85 × 153
HCF = (85 × 153) / LCM
HCF = (85 × 153) / 765
HCF = 17
Hence, the HCF of 85 and 153 is 17.
Frequently Asked Questions on HCF of 85 and 153
What is the HCF of 85 and 153?
What are the methods used to find the HCF of 85 and 153?
There are three methods to find the HCF of 85 and 153. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Which of the following is the HCF of 85 and 153? 11, 17, 25, 29.
Find the LCM if the HCF of 85 and 153 is 17.
We know that
HCF × LCM = 85 × 153
Given
HCF = 17
17 × LCM = 85 × 153
LCM = 765
Hence, the LCM is 765
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