The HCF of 24 and 36 is 12. HCF is the greatest number that can divide 24 and 36 without having any remainder. HCF stands for Highest Common Factor. As the name suggests, for a given set of numbers 24 and 36, there would be common factors, and the highest among the common factors is known as the HCF. In the given set of numbers 24 and 36, the common factors are 1, 2, 3, 4, 6 and 12. Since 12 is the highest among the given factors, HCF or Highest common factor of 24 and 36 would be 12. HCF is also termed as GCF, which is the Greatest Common Factor. Learn more on HCF.
What is the HCF of 24 and 36?
The Highest Common Factor, also known as the Greatest Common Factor, of 24 and 36 is 12.
How to Find HCF of 24 and 36?
There are three methods to find the HCF of 24 and 36:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 24 and 36 by Prime Factorisation Method
In the Prime Factorisation method, the given numbers will be expressed as the product of prime numbers. Here, 24 and 36 can be expressed as;
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common prime factors of 24 and 36 are 2, 2, 3. Therefore HCF will be,
HCF (24, 36) = 2 × 2 × 3 = 12.
HCF of 24 and 36 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 lesser number or the other number is next divided by the remainder of the previous division. This step is repeated until 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 24 and 36, the HCF by long division method is;
HCF (24, 36) = 12
HCF of 24 and 36 by Listing the Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, and that would be the HCF. Below is the list of factors for 24 and 36.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, HCF (24, 36) = 12
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Video Lesson on Properties of HCF and LCM
Solved Examples
Find the greatest number that divides 2 and 12.
Solution: Factors of 2 are 1 and 2.
Factors of 12 are 1, 2, 3, 4, 6 and 12.
Common Factors of 2 and 12 are 1 and 2. The Greatest Common Factor is 2. Hence, 2 is the GCF of 2 and 12.
Two ribbons are 5 cm and 10 cm long. The ribbons are cut into pieces of equal length. What will be the maximum length of each piece?
Solution: Maximum length of each ribbon piece is nothing but the HCF.
HCF of 5 and 10 is
5 = 1 × 5
10 = 2 × 5
Common Factor of 5 and 10 is 5. Hence, each piece should be 5 cm.
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