The HCF of 9 and 15 is 3. HCF stands for Highest Common Factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD, Greatest Common Divisor or GCF, Greatest Common Factor. For the given set of numbers 9 and 15, 3 is the HCF/GCD/GCF. The common factors for 9 and 15 are 1 and 3 only. Since 3 is greater than 1, the HCF of 9 and 15 is 3. You can refer to the Highest Common Factor for more details.
What is the HCF of 9 and 15?
The Highest Common Factor, also known as the Greatest Common Factor, of 9 and 15 is 3.
How to Find HCF of 9 and 15?
There are three methods to find the HCF of 9 and 15:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 9 and 15 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 9 and 15 can be expressed as:
9 = 3 × 3
15 = 3 × 5
The only common prime factor is 3.
Therefore, HCF (9, 15) = 3.
HCF of 9 and 15 by Long Division Method
In the long division method, the following steps are followed.
- From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
- In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor.
- The above step is followed until the remainder is zero.
- The last divisor would be the HCF.
For 9 and 15, the HCF by long division method is:
Hence, HCF (9, 15) = 3
HCF of 9 and 15 by Listing Common Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 9 and 15:
Factors of 9: 1, 3 and 9
Factors of 15: 1, 2, 3, 5 and 15.
The common factors of 9 and 15 are 1 and 3.
Therefore, HCF (9, 15) = 3
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the Greatest number that divides 9 and 15 equally?
The Greatest number that divides 9 and 15 equally is nothing but GCF/HCF, which is 3 for 9 and 15.
2. What is the GCF of 30 and 60?
The GCF of 30 and 60 is 30.
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