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The Highest Common Common (HCF) of numbers is the highest possible quantity that precisely divides both the numbers. The maximum commonplace aspect (HCF) is also referred to as the greatest not unusual divisor (GCD). Click here

There are numerous methods to find the HCF of numbers. The fastest way to discover the HCF of two or extra numbers is using the prime factorization method. Explore the world via exclusive factors and qualities of HCF. Find solutions to questions like what is the highest not unusual aspect for a set of numbers, easy ways to calculate HCF, HCF via department technique, its relation to LCM, and discover greater interesting statistics around them.

HCF Definition

The HCF (Highest Common Factor) of two or extra numbers is the greatest wide variety amongst all the common factors of the given numbers. In simple words, the HCF (highest not unusual component) of herbal numbers x and y is the finest feasible variety that divides both x and y. Let us apprehend this definition the usage of numbers, 18 and 27. Nine is the largest (largest) number among these numbers. So, the HCF of 18 and 27 is 9. This is written as: HCF(18, 27) = nine. Observe the subsequent figure to understand this concept.

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HCF Example

Using the definition above, the HCF of a few sets of numbers may be listed as follows:

  • HCF of 60 and forty is 20, i.E. HCF(60, 40) = 20
  • HCF of one hundred and one hundred fifty is 50, i.E. HCF(a hundred and fifty, 50) = 50
  • HCF of a hundred and forty-four and 24 is 24, i.E. HCF(a hundred and forty-four, 24) = 24
  • HCF of 17 and 89 is 1, i.E. HCF(17, 89) = 1

How To Find HCF?

There are many ways to find the highest not the unusual aspect of a given wide variety. Whatever the approach, the answer to the HCF of numbers will constantly be identical. There are three methods of computing the HCF of  numbers:

  • HCF through Listing Factor Method
  • HCF by using prime factorization
  • HCF by using a department approach

Let us talk about each technique in element with the assistance of examples.

HCF Via Listing Factors Method

In this approach, we list the factors of each wide variety and find the not unusual elements of these numbers. Then, for many of the commonplace elements, we decide on the best common aspect. Let us understand this approach through the use of an instance.

Example: Find the HCF of 30 and forty-two.

Solution: We will list the factors of 30 and forty-two. The elements of 30 are 1, 2, three, five, 6, 10, 15, and 30 and the elements of 42 are 1, 2, 3, 6, 7, 14. , 21, and 42. 1, 2, three, and six are common factors of 30 and forty-two. But 6 is the finest of all commonplace elements. 

HCF Through Prime Factorization

To locate the HCF of numbers using the method of high factorization, we use the subsequent steps. Let us understand this approach through the usage of the example given underneath.

  • Step 1: Find the common high factors of the given numbers.
  • Step 2: Then, multiply those not unusual high factors to get the HCF of those numbers.

Example: Find the HCF of 60 and ninety.

Solution: Prime factors of 60 = 2 × 2 × three × 5; and top elements of ninety = 2 × 3 × 3 × five. Now, the HCF of 60 and 90 may be made from the not unusual elements, which are 2, 3, and five. Hence, HCF of 60 and ninety = 2 × 3 × five = 30

HCF By Division Method

The HCF of two numbers can be calculated using the department approach. Let us understand this by the use of the following steps and the example given beneath.

  • Step 1: In this method, we divide the larger variety through the smaller quantity and test the remainder.
  • Step 2: Then, we make the remainder of the previous step the new divisor; And the divisor of the preceding step turns into the brand new dividend. After that, we do a lengthy division again.
  • Step three: We hold the long division technique until we get a remainder of zero. It should be noted that the final divisor can be the HCF of these two numbers.

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