A day full of math games & activities. Find one near you.

HCF of 145 and 232

HCF of 145 and 232 is the largest possible number that divides 145 and 232 exactly without any remainder. The factors of 145 and 232 are 1, 5, 29, 145 and 1, 2, 4, 8, 29, 58, 116, 232 respectively. There are 3 commonly used methods to find the HCF of 145 and 232 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 145 and 232
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 145 and 232?

Answer: HCF of 145 and 232 is 29.

Explanation:

The HCF of two non-zero integers, x(145) and y(232), is the highest positive integer m(29) that divides both x(145) and y(232) without any remainder.

Methods to Find HCF of 145 and 232

Let's look at the different methods for finding the HCF of 145 and 232.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 145 and 232 by Long Division

HCF of 145 and 232 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 232 (larger number) by 145 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (145) by the remainder (87).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (29) is the HCF of 145 and 232.

HCF of 145 and 232 by Listing Common Factors

Factors of 145: 1, 5, 29, 145
Factors of 232: 1, 2, 4, 8, 29, 58, 116, 232

There are 2 common factors of 145 and 232, that are 1 and 29. Therefore, the highest common factor of 145 and 232 is 29.

HCF of 145 and 232 by Prime Factorization

Prime factorization of 145 and 232 is (5 × 29) and (2 × 2 × 2 × 29) respectively. As visible, 145 and 232 have only one common prime factor i.e. 29. Hence, the HCF of 145 and 232 is 29.

☛ Also Check:

HCF of 145 and 232 Examples

Example 1: For two numbers, HCF = 29 and LCM = 1160. If one number is 145, find the other number.

Solution:

Given: HCF (y, 145) = 29 and LCM (y, 145) = 1160
∵ HCF × LCM = 145 × (y)
⇒ y = (HCF × LCM)/145
⇒ y = (29 × 1160)/145
⇒ y = 232
Therefore, the other number is 232.
Example 2: Find the highest number that divides 145 and 232 exactly.

Solution:

The highest number that divides 145 and 232 exactly is their highest common factor, i.e. HCF of 145 and 232.
⇒ Factors of 145 and 232:
- Factors of 145 = 1, 5, 29, 145
- Factors of 232 = 1, 2, 4, 8, 29, 58, 116, 232
Therefore, the HCF of 145 and 232 is 29.
Example 3: The product of two numbers is 33640. If their HCF is 29, what is their LCM?

Solution:

Given: HCF = 29 and product of numbers = 33640
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 33640/29
Therefore, the LCM is 1160.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 145 and 232

What is the HCF of 145 and 232?

The HCF of 145 and 232 is 29. To calculate the HCF of 145 and 232, we need to factor each number (factors of 145 = 1, 5, 29, 145; factors of 232 = 1, 2, 4, 8, 29, 58, 116, 232) and choose the highest factor that exactly divides both 145 and 232, i.e., 29.

If the HCF of 232 and 145 is 29, Find its LCM.

HCF(232, 145) × LCM(232, 145) = 232 × 145
Since the HCF of 232 and 145 = 29
⇒ 29 × LCM(232, 145) = 33640
Therefore, LCM = 1160
☛ Highest Common Factor Calculator

How to Find the HCF of 145 and 232 by Prime Factorization?

To find the HCF of 145 and 232, we will find the prime factorization of the given numbers, i.e. 145 = 5 × 29; 232 = 2 × 2 × 2 × 29.
⇒ Since 29 is the only common prime factor of 145 and 232. Hence, HCF (145, 232) = 29.
☛ What is a Prime Number?

What are the Methods to Find HCF of 145 and 232?

There are three commonly used methods to find the HCF of 145 and 232.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 145 and 232 by Long Division Method?

To find the HCF of 145, 232 using long division method, 232 is divided by 145. The corresponding divisor (29) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 145, 232?

The following equation can be used to express the relation between Least Common Multiple and HCF of 145 and 232, i.e. HCF × LCM = 145 × 232.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum