The HCF of 145 and 232 is 29. The Highest Common Factor (HCF) of 145 and 232 is the largest number that divides both 145 and 232 evenly. The article HCF designed by expert faculty at BYJU’S helps students improve their logical approach and rational thinking abilities, which are vital in solving problems more effectively. This article provides in-depth information on Highest Common Factor in simple language so that students understand the concept effortlessly. In this article, let us grasp the tricks of how to find the Highest Common Factor of 145 and 232 using different methods.
What is the HCF of 145 and 232?
The answer to this question is 29. The factors of 145 and 232 are 1, 5, 29, 145, and 1, 2, 4, 8, 29, 58, 116, 232, respectively. Here, the Highest Common Factor of 145 and 232 is 29.
How to Find HCF of 145 and 232?
There are three methods to find the HCF of 145 and 232:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 145 and 232 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).
145 = 5 × 29
232 = 2 × 2 × 2 × 29
The Common prime factor of 145 and 232 is 29.
Therefore,
HCF of (145, 232) = 29
HCF of 145 and 232 by Long Division Method
In this method, we use the following steps to determine the Highest Common Factor of 145 and 232.
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.
The HCF of 145 and 232 by the long division method is:
HCF (145, 232) = 29
HCF of 145 and 232 by Listing Common Factors
In this method, we can determine the Highest Common Factor by listing all the factors of given numbers. The factors of 145 and 232 are as follows:
Factors of 145: 1, 5, 29, 145
Factors of 232: 1, 2, 4, 8, 29, 58, 116, 232
Hence, HCF (145, 232) = 29
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 145 and 232 exactly?
Solution: The largest number that divides both 145 and 232 is their Highest Common Factor (HCF). 29 is the Highest Common Factor of 145 and 232. Hence, 29 is the highest number that divides both 145 and 232 exactly.
2. The product of two numbers is 33640. Find their LCM if their HCF is 29.
Solution: Given
HCF = 29
Product of numbers = 33640
We know that,
LCM × HCF = Product of numbers
LCM = Product of numbers/HCF
LCM = 33640/29
LCM = 1160
Hence, the LCM is 1160.
Frequently Asked Questions on HCF of 145 and 232
What is the HCF of 145 and 232?
What are the methods used to find the HCF of 145 and 232?
There are three methods to find the HCF of 145 and 232. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Is the HCF of 145 and 232 same as the LCM of 145 and 232?
Write the relation between LCM and HCF of 145 and 232.
The below equation is used to express the relation between LCM and HCF of 145 and 232
HCF × LCM = 145 × 232
Calculate the LCM if the HCF of 145 and 232 is 29.
We know that
HCF × LCM = 145 × 232
Given
HCF = 29
29 × LCM = 145 × 232
LCM = 1160
Therefore, the LCM is 1160
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