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HCF of 10 and 15

HCF of 10 and 15 is the largest possible number that divides 10 and 15 exactly without any remainder. The factors of 10 and 15 are 1, 2, 5, 10 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the HCF of 10 and 15 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 10 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 10 and 15?

Answer: HCF of 10 and 15 is 5.

Explanation:

The HCF of two non-zero integers, x(10) and y(15), is the highest positive integer m(5) that divides both x(10) and y(15) without any remainder.

Methods to Find HCF of 10 and 15

The methods to find the HCF of 10 and 15 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 10 and 15 by Prime Factorization

Prime factorization of 10 and 15 is (2 × 5) and (3 × 5) respectively. As visible, 10 and 15 have only one common prime factor i.e. 5. Hence, the HCF of 10 and 15 is 5.

HCF of 10 and 15 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 3, 5, 15

There are 2 common factors of 10 and 15, that are 1 and 5. Therefore, the highest common factor of 10 and 15 is 5.

HCF of 10 and 15 by Long Division

HCF of 10 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 15 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 10 and 15.

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HCF of 10 and 15 Examples

Example 1: The product of two numbers is 150. If their HCF is 5, what is their LCM?

Solution:

Given: HCF = 5 and product of numbers = 150
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 150/5
Therefore, the LCM is 30.
Example 2: Find the HCF of 10 and 15, if their LCM is 30.

Solution:

∵ LCM × HCF = 10 × 15
⇒ HCF(10, 15) = (10 × 15)/30 = 5
Therefore, the highest common factor of 10 and 15 is 5.
Example 3: Find the highest number that divides 10 and 15 exactly.

Solution:

The highest number that divides 10 and 15 exactly is their highest common factor, i.e. HCF of 10 and 15.
⇒ Factors of 10 and 15:
- Factors of 10 = 1, 2, 5, 10
- Factors of 15 = 1, 3, 5, 15
Therefore, the HCF of 10 and 15 is 5.

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FAQs on HCF of 10 and 15

What is the HCF of 10 and 15?

The HCF of 10 and 15 is 5. To calculate the Highest common factor of 10 and 15, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 15 = 1, 3, 5, 15) and choose the highest factor that exactly divides both 10 and 15, i.e., 5.

How to Find the HCF of 10 and 15 by Prime Factorization?

To find the HCF of 10 and 15, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 15 = 3 × 5.
⇒ Since 5 is the only common prime factor of 10 and 15. Hence, HCF (10, 15) = 5.
☛ What are Prime Numbers?

How to Find the HCF of 10 and 15 by Long Division Method?

To find the HCF of 10, 15 using long division method, 15 is divided by 10. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 10, 15?

The following equation can be used to express the relation between Least Common Multiple and HCF of 10 and 15, i.e. HCF × LCM = 10 × 15.

If the HCF of 15 and 10 is 5, Find its LCM.

HCF(15, 10) × LCM(15, 10) = 15 × 10
Since the HCF of 15 and 10 = 5
⇒ 5 × LCM(15, 10) = 150
Therefore, LCM = 30
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 10 and 15?

There are three commonly used methods to find the HCF of 10 and 15.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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