The HCF of 36 and 144 is 36. The HCF of 36 and 144 is the greatest integer that can divide both numbers evenly. HCF stands for Highest Common Factor. As the name suggests, for a given set of numbers, there would be common factors, and the highest among the common factors is known as the HCF. In the given set of numbers 36 and 144, the common factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Since 36 is the highest among the given factors, HCF would be 36 for 36 and 144. HCF is also termed as GCF which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 36 and 144?
The Highest Common Factor, also known as the Greatest Common Factor, of 36 and 144 is 36.
How to Find HCF of 36 and 144?
There are three methods to find the HCF of 36 and 144:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 36 and 144 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 36 and 144 can be expressed as:
36 = 2 × 2 × 3 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
Common prime factors are 2, 2, 3 and 3.
Therefore, HCF (36, 144) = 2 × 2 × 3 × 3 = 36.
HCF of 36 and 144 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 36 and 144, the HCF by long division method is:
Therefore, HCF (36, 144) = 36
HCF of 36 and 144 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 36 and 144:
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 144:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, HCF (36, 144) = 36
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Solved Examples
- Find the HCF of 2, 12 and 36 using listing factors.
Solution:
Factors of 2 are 1 and 2.
Factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors of 2, 12 and 36 are 1 and 2.
Therefore, HCF of 2, 12 and 36 is 2.
2. What is the second highest common factor of 36 and 144?
Solution: The second highest common factor of 36 and 144 is 18.
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