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

HCF of 87 and 145

HCF of 87 and 145 is the largest possible number that divides 87 and 145 exactly without any remainder. The factors of 87 and 145 are 1, 3, 29, 87 and 1, 5, 29, 145 respectively. There are 3 commonly used methods to find the HCF of 87 and 145 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 87 and 145
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 87 and 145?

Answer: HCF of 87 and 145 is 29.

Explanation:

The HCF of two non-zero integers, x(87) and y(145), is the highest positive integer m(29) that divides both x(87) and y(145) without any remainder.

Methods to Find HCF of 87 and 145

Let's look at the different methods for finding the HCF of 87 and 145.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 87 and 145 by Long Division

HCF of 87 and 145 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 145 (larger number) by 87 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (87) by the remainder (58).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (29) is the HCF of 87 and 145.

HCF of 87 and 145 by Prime Factorization

Prime factorization of 87 and 145 is (3 × 29) and (5 × 29) respectively. As visible, 87 and 145 have only one common prime factor i.e. 29. Hence, the HCF of 87 and 145 is 29.

HCF of 87 and 145 by Listing Common Factors

Factors of 87: 1, 3, 29, 87
Factors of 145: 1, 5, 29, 145

There are 2 common factors of 87 and 145, that are 1 and 29. Therefore, the highest common factor of 87 and 145 is 29.

☛ Also Check:

HCF of 87 and 145 Examples

Example 1: Find the highest number that divides 87 and 145 exactly.

Solution:

The highest number that divides 87 and 145 exactly is their highest common factor, i.e. HCF of 87 and 145.
⇒ Factors of 87 and 145:
- Factors of 87 = 1, 3, 29, 87
- Factors of 145 = 1, 5, 29, 145
Therefore, the HCF of 87 and 145 is 29.
Example 2: For two numbers, HCF = 29 and LCM = 435. If one number is 87, find the other number.

Solution:

Given: HCF (x, 87) = 29 and LCM (x, 87) = 435
∵ HCF × LCM = 87 × (x)
⇒ x = (HCF × LCM)/87
⇒ x = (29 × 435)/87
⇒ x = 145
Therefore, the other number is 145.
Example 3: The product of two numbers is 12615. If their HCF is 29, what is their LCM?

Solution:

Given: HCF = 29 and product of numbers = 12615
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 12615/29
Therefore, the LCM is 435.

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 87 and 145

What is the HCF of 87 and 145?

The HCF of 87 and 145 is 29. To calculate the Highest common factor of 87 and 145, we need to factor each number (factors of 87 = 1, 3, 29, 87; factors of 145 = 1, 5, 29, 145) and choose the highest factor that exactly divides both 87 and 145, i.e., 29.

What is the Relation Between LCM and HCF of 87, 145?

The following equation can be used to express the relation between LCM and HCF of 87 and 145, i.e. HCF × LCM = 87 × 145.

What are the Methods to Find HCF of 87 and 145?

There are three commonly used methods to find the HCF of 87 and 145.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 87 and 145 by Prime Factorization?

To find the HCF of 87 and 145, we will find the prime factorization of the given numbers, i.e. 87 = 3 × 29; 145 = 5 × 29.
⇒ Since 29 is the only common prime factor of 87 and 145. Hence, HCF (87, 145) = 29.
☛ Prime Number

If the HCF of 145 and 87 is 29, Find its LCM.

HCF(145, 87) × LCM(145, 87) = 145 × 87
Since the HCF of 145 and 87 = 29
⇒ 29 × LCM(145, 87) = 12615
Therefore, LCM = 435
☛ Highest Common Factor Calculator

How to Find the HCF of 87 and 145 by Long Division Method?

To find the HCF of 87, 145 using long division method, 145 is divided by 87. The corresponding divisor (29) when remainder equals 0 is taken as HCF.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum