The HCF of 96 and 404 is 4. HCF is the greatest integer that can divide 96 and 404 evenly, and that number is 4. HCF stands for Highest Common Factor, and it is also known as GCF, Greatest Common Factor or GCD, Greatest Common Divisor. For a given set of numbers, there would be common factors, and the highest among the common factors is known as the HCF. For 96 and 404, the common factors are 1, 2 and 4. Since 4 is the highest among the given factors, HCF would be 4 for 96 and 404. You can refer to GCF for more details.
What is the HCF of 96 and 404?
The Highest Common Factor, also known as the Greatest Common Factor, of 96 and 404 is 4.
How to Find HCF of 96 and 404?
There are three methods to find the HCF of 96 and 404:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 96 and 404 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 96 and 404 can be expressed as;
96 = 2 × 2 × 2 × 2 × 2 × 3
404 = 2 × 2 × 101
Common prime factors of 96 and 404 are 2 and 2. Therefore HCF will be,
HCF (96, 404) = 2 × 2 = 4.
HCF of 96 and 404 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.
HCF of 96 and 404 by the Long Division method is;
HCF (96, 404) = 4
HCF of 96 and 404 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 96 and 404:
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Factors of 404: 1, 2, 4, 101, 202, 404.
Therefore, HCF (96, 404) = 4
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Video Lesson on Properties of HCF and LCM
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Solved Examples
Find the greatest number that divides 4 and 16?
Solution: Factors of 4 are 1, 2 and 4.
Factors of 16 are 1, 2, 4, 8 and 16.
Common Factors of 4 and 16 are 1, 2 and 4. The Greatest Common Factor is 4. Hence, 4 is the GCF of 4 and 16.
What is the GCF of 16 and 32?
Solution: GCF of 16 and 32 is 16.
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