The HCF of 30 and 48 is 6. HCF is the greatest integer that can divide 30 and 48 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 30 and 48, the common factors are 1, 2, 3 and 6. Since 6 is the highest among the given factors, HCF would be 6 for 30 and 48. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on HCF.
What is the HCF of 30 and 48?
The Highest Common Factor, also known as the Greatest Common Factor of 30 and 48, is 6.
How to Find HCF of 30 and 48?
There are three methods to find the HCF of 30 and 48:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 30 and 48 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 30 and 48 can be expressed as:
30 = 2 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3
The common prime factors of 30 and 48 are 2 × 3. Therefore, HCF will be:
HCF (30, 48) = 2 × 3 = 6
HCF of 30 and 48 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 30 and 48, the HCF by long division method is:
Therefore, HCF (30, 48) = 6
HCF of 30 and 48 by Listing Common Factors
By listing common factors of given numbers, we can identify the Highest/Greatest/Biggest Common Factor, which is the HCF. Below is the list of factors for 30 and 48.
Factors of 30: 1, 2, 3, 5, 6, 6, 10, 15, 30
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, HCF (30, 48) = 6
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the greatest number that divides 6 and 36?
Solution: The common factors of 6 and 36 are 1, 3, and 6. The Greatest Common Factor is 6. Hence, 6 is the greatest number that divides 6 and 36.
2. What is the HCF of 9 and 99?
Solution: The HCF of 9 and 99 is 9.
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