The HCF of 15 and 27 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 15 and 27, 3 is the HCF/GCD/GCF. The common factors for 15 and 27 are 1 and 3. You can refer to the Highest Common Factor for more details.
What is the HCF of 15 and 27?
The Highest Common Factor, also known as the Greatest Common Factor, of 15 and 27 is 3.
How to Find HCF of 15 and 27?
There are three methods to find the HCF of 15 and 27:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 15 and 27 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 15 and 27 can be expressed as:
15 = 3 × 5
27 = 3 × 3 × 3
The only common prime factor is 3.
Therefore, HCF (15, 27) = 3.
HCF of 15 and 27 by Long Division Method
In the long division method, from the given set of numbers, the smaller number is used as the divisor to the larger number. The smaller number is divided by the remainder. This step is repeated till the remainder becomes zero.
Detailed steps are as follows:
- 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 15 and 27, the HCF by long division method is:
Therefore, HCF (15, 27) = 3
HCF of 15 and 27 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 15 and 27:
Factors of 15: 1, 3, 5 and 15.
Factors of 27: 1, 3, 9 and 27.
Therefore, HCF (15, 27) = 3
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the greatest number that divides 13 and 39 evenly.
Solution: The greatest number that divides 13 and 39 evenly is the Greatest Common Factor, which is 13.
2. What is the HCF of 9 and 27?
Solution: The HCF of 9 and 27 is 9.
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