The HCF of 81 and 237 is 3. The factors of 81 and 237 are 1, 3, 9, 27, 81, and 1, 3, 79, 237, respectively. From all the factors of 81 and 237, 3 is the largest number. Hence, we can conclude that the Highest Common Factor of 81 and 237 is 3. To master the HCF concept, students can rely on the article HCF of Two Numbers prepared by BYJU’S teachers. The HCF of given numbers can be calculated using prime factorisation, long division method and listing common factors. Let us have a look at how to determine the Highest Common Factor of 81 and 237 with solved examples and FAQs here.
What is the HCF of 81 and 237?
The Highest Common Factor of 81 and 237 is 3. The common factors of 81 and 237 are 1 and 3. Hence, the Highest Common Factor of 81 and 237 is 3.
How to Find HCF of 81 and 237?
There are three methods to find the HCF of 81 and 237:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 81 and 237 by Prime Factorisation Method
In the prime factorisation, to verify the HCF, we express the given numbers as the product of prime factors. Hence, 81 and 237 can be expressed as:
81 = 3 × 3 × 3 × 3
237 = 3 × 79
The common prime factor of 81 and 237 is 3.
Therefore,
HCF (81, 237) = 3
HCF of 81 and 237 by Long Division Method
We can determine the HCF of 81 and 237 by using the following steps:
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 equal to zero. The last divisor will be the HCF of the given two numbers.
For 81 and 237, the HCF by the long division method is:
HCF (87, 237) = 3
HCF of 81 and 237 by Listing Common Factors
In this method, we find the HCF of 81 and 237 by listing out the common factors. The factors of 81 and 237 are given below:
Factors of 81: 1, 3, 9, 27, 81
Factors of 237:1, 3, 79, 237
Hence, HCF (81, 237) = 3
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 81 and 237 exactly?
Solution: The largest that divides both 81 and 237 is their Highest Common Factor(HCF). The HCF of 81 and 237 is 3. Therefore, 3 is the highest number that divides both 81 and 237 exactly.
2. The product of two numbers is 19197. What is the LCM if their HCF is 3?
Solution: Given
HCF = 3
Product of numbers = 19197
We know that
LCM × HCF = Product of numbers
LCM = Product of numbers/HCF
LCM = 19197 / 3
LCM = 6399
Hence the LCM is 6399.
Frequently Asked Questions on HCF of 81 and 237
What is the HCF of 81 and 237?
Is the HCF of 81 and 237 the same as the HCF of 3 and 27?
What are the common factors of 81 and 237?
Mention the methods used to find the HCF of 81 and 237.
The methods used to find the HCF of 81 and 237 are as follows:
Prime Factorisation
Long Division method
Listing common factors
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