The HCF of 3 and 15 is 3. The greatest factor present in between given two or more numbers is defined as the Highest Common Factor (HCF). Generally, to find the HCF of given numbers, we use the methods such as prime factorisation, long division method and listing common factors. HCF of Two Numbers is a vital study source to obtain an in-depth knowledge of the HCF concept. Teachers who hold years of experience have drafted this article with the aim of helping students in their learning process. In this article, let us learn the simple technique of how to determine the Highest Common Factor of 3 and 15 in an accurate manner.
What is the HCF of 3 and 15?
The Highest Common Factor (HCF) of 3 and 15 is 3. Therefore, the largest number that divides 3 and 15 completely is 3. The factors of 3 are 1, 3, and the factors of 15 are 1, 3, 5, 15.
How to Find HCF of 3 and 15?
The methods used to find the HCF of 3 and 15 are as follows:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 3 and 15 by Prime Factorisation Method
In prime factorisation, the numbers can be written as the product of prime factors. Thus, the numbers 3 and 15 can be written as:
3 = 3
15 = 3 × 5
The common prime factor of 3 and 15 is 3.
Therefore,
HCF of (3, 15) = 3
HCF of 3 and 15 by Long Division Method
In the long division method, we use the following steps to find the HCF of 3 and 15:
Step 1: Divide the largest number by the smallest among the given two numbers.
Step 2: Check the remainder; if it is not zero, then make it a new divisor and mention the previous divisor as the new dividend and continue the division process.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor is considered the HCF of the given two numbers.
The HCF of 3 and 15 by using the long division method is shown below:
HCF (3, 15) = 3
HCF of 3 and 15 by Listing Common Factors
We list all the factors of given numbers to determine their Highest Common Factor in this method. The following are the factors of 3 and 15:
Factors of 3: 1, 3
Factors of 15: 1, 3, 5, 15
Thus, HCF (3, 15) = 3
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the HCF of 3 and 15 if their LCM is 15?
Solution: We know that
LCM × HCF = 3 × 15
15 × HCF = 3 × 15
HCF = 3
Therefore, the HCF of 3 and 15 is 3.
2. Calculate the LCM if the product of two numbers is 45 and their HCF is 3.
Solution: Given
HCF = 3
Product of numbers = 45
We know that
LCM × HCF = Product of numbers
LCM × 3 = 45
LCM = 15
Therefore, the LCM is 15.
Frequently Asked Questions on HCF of 3 and 15
Write the HCF of 3 and 15.
List the methods used to find the HCF of 3 and 15.
The below-given methods are used to find the HCF of 3 and 15.
Prime Factorisation
Long Division Method
Listing Common Factors
Is the HCF of 3 and 15 same as the HCF of 3 and 27?
What is the LCM if the HCF of 3 and 15 is 3?
We know that
HCF × LCM = 3 × 15
Given
HCF = 3
3 × LCM = 3 × 15
LCM = 15
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