The HCF of 15 and 18 is 3. HCF of 15 and 18 is the greatest integer that can divide both numbers evenly. HCF stands for Highest Common Factor. For a given set of numbers, there would be common factors, and as the name suggests, the highest among the common factors is known as the HCF. In the given set of numbers 15 and 18, the common factors are 1 and 3. Since 3 is the highest among the common factors, HCF would be 3 for 15 and 18. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on HCF.
What is the HCF of 15 and 18?
The Highest Common Factor, also known as the Greatest Common Factor, of 15 and 18 is 3.
How to Find HCF of 15 and 18?
There are three methods to find the HCF of 15 and 18:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 15 and 18 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 15 and 18 can be expressed as:
15 = 3 × 5
18 = 2 × 3 × 3
Common prime factors are 1 and 3. Therefore, HCF will be,
HCF (15, 18) = 1 × 3 = 3.
HCF of 15 and 18 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 18, the HCF by Long Division method is:
Therefore, HCF (15, 18) = 3
HCF of 15 and 18 by Listing 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 18:
Factors of 15: 1, 3, 5 and 15
Factors of 18: 1, 2, 3, 6, 9 and 18
Therefore, HCF (15, 18) = 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 15 and 18.
The greatest number that divides 15 and 18 is nothing but the GCF, which is 3.
2.What is the HCF for 3, 6 and 18?
The HCF for 3, 6 and 18 is 3, as 3 is the smallest number among the given set of numbers and also the factor for 6 and 18.
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