The HCF of 12 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 12 and 15, 3 is the HCF/GCD/GCF. 12 and 15 have only 2 common factors, and they are 1 and 3, out of which 3 is the highest. Hence, 3 is the HCF of 12 and 15. You can refer to the Highest Common Factor for more details.
What is the HCF of 12 and 15?
The Highest Common Factor, also known as the Greatest Common Factor, of 12 and 15 is 3.
How to Find HCF of 12 and 15?
There are three methods to find the HCF of 12 and 15:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12 and 15 by Prime Factorisation Method
In Prime Factorisation, the numbers can be expressed as the product of prime numbers. Here, 12 and 15 can be expressed as;
12 = 2 × 2 × 3
15 = 3 × 5
Common Prime Factor is 3. Therefore, HCF will be,
HCF (12, 15) = 3.
HCF of 12 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 12 and 15, the HCF by Long Division method is;
Hence, HCF (12, 15) = 3
HCF of 12 and 15 by Listing the 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 12 and 15:
Factors of 12: 1, 2, 3, 4, 6, and 12
Factors of 15: 1, 3, 5, and 15.
Therefore, HCF (12, 15) = 3
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Video Lesson on Properties of HCF and LCM
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Solved Examples
1. Find the greatest number that divides 12 and 15.
Factors of 12 are 1, 2, 3, 4, 6, and 12.
Factors of 15 are 1, 3, 5, and 15.
Common Factors are 1 and 3. The Greatest Common Factor is 3. Hence, 3 is the greatest number that divides 12 and 15.
2. What is the GCF of 12 and 18?
GCF of 12 and 18 is 6.
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