To calculate HCF (Highest Common Factor) in Class 10, there are two methods that can be used – Prime Factorization Method and Division Method.
Prime Factorization Method:
In this method, both the numbers are divided by prime factors. The greatest common factor (GCF) is determined by multiplying the common factors.
For example, to calculate the HCF of 12 and 16,
Step 1: Find prime factors of 12 and 16:
12 = 2 x 2 x 3
16 = 2 x2 x2 x2
Step 2: Identify common factors:
In this case, both numbers (12 and 16) have a factor of 2.
Step 3: Calculate HCF:
We just take the common factors, in this case ‘2’ and multiply them, to get the HCF. Therefore, the HCF of 12 and 16 = 2 x 2 = 4
Division Method:
In this method, the larger number is divided by the smaller number and the remainder is again divided by the divisor. The process is repeated until no remainder is obtained and the divisor is the HCF.
For example, to calculate the HCF of 30 and 45,
Step 1: Divide 30 by 45:
Remainder = 30 – (45 x 0) = 30
Step 2: Divide 45 by 30:
Remainder = 45 – (30 x 1) = 15
Step 3: Divide 30 by 15:
Remainder = 30 – (15 x 2) = 0
Therefore, the divisor is the HCF, which is 15.
In conclusion, either of the two methods – Prime Factorization Method or Division Method – can be used to calculate the HCF for any given numbers in Class 10.
How do you do HCF step by step?
Step 1: Make sure both numbers are whole, rational numbers (they can be positive or negative).
Step 2: Factor each number into primes. In order to do this, you can use a factor tree, or a decomposition into prime factors.
Step 3: Make a list of all the factors present in both numbers. For example, if the numbers are 24 and 64, the list of factors for each would be:
24 – 2, 2, 2, 3
64 – 2, 2, 2, 2, 2, 2, 3
Step 4: Find the highest common factor by going through the list, finding the highest number that appears in both lists. In this case, it is 3, so 3 is the highest common factor.
What is the easiest way to calculate HCF?
The easiest way to calculate the highest common factor (HCF) is to use the prime factorization method. This involves breaking down both numbers into prime factors and then finding the highest prime factor which is common to both numbers.
The HCF of two numbers is the product of those common prime factors. To find the prime factors, begin with the smallest prime number – 2 – and keep dividing the number with the prime numbers until it becomes 1.
Once the prime factorization is complete, all the prime factors for each number should be listed out. The highest common prime factors should be identified and the HCF is obtained by multiplying all the common prime factors together.
What are the 3 methods of HCF?
The three common methods of finding the Highest Common Factor (HCF) are the Prime Factorization Method, the Division Method, and the Euclidean Algorithm.
The Prime Factorization Method is used to determine the HCF of two or more numbers by writing each number as a product of its prime factors. The highest prime factor that appears in each expression is then identified and multiplied together to determine the HCF of the given numbers.
The Division Method is a simple approach to finding the HCF of two numbers. To use this method, one number is divided by the other and then repeated for any remainder until the remainder is zero. The factor in the last division is the HCF of the two numbers.
The Euclidean Algorithm is a method used to identify the HCF of two numbers and is considered the most efficient method due to its simple algorithmic and recursive nature. The algorithm involves subtracting the smaller number from the larger one, and then again repeating this process with the result and the smaller number, until one of the numbers become zero.
The other number at this stage, in which one of the numbers is zero, is the HCF of the two numbers.
How do you do HCF in maths examples?
The highest common factor (HCF) of two or more given numbers is the highest number that divides them all without a remainder. To find the HCF, you can use either the prime factorization or the division method.
Prime factorization is finding out which prime numbers of a number’s prime factors. To do this, you simply factorize all the numbers into prime numbers. For example, the prime factors of 24 are 2 x 2 x 2 x 3.
The division method is to take the larger of the two numbers and then divide it by the smaller one. Keep dividing by the same number until the remainder is 0. The number used as the divisor will be the HCF.
For example, to find the HCF of 24 and 12:
•Take the larger number, 24, and divide it by the smaller number, 12. The result is 24 / 12 = 2.
•Take the result of that calculation, which is 2, and divide it by 12. The result is 2 / 12 = 0 remainder.
•Therefore, the highest common factor of 24 and 12 is 12.
How do you find the HCF of 24 and 36?
To find the Highest Common Factor (HCF) of 24 and 36, we can use the prime factorisation method. First, we prime factorise 24 and 36, listing out the prime numbers that are multiplied together to give the original numbers.
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
We then list out all of the prime numbers, and see how many times each prime number is repeated across the factorisation of both numbers. In this case, both 24 and 36 have two 2s and two 3s. We then multiply these prime numbers together to find the highest common factor.
2 x 2 x 3 x 3 = 36, meaning that the highest common factor (HCF) of 24 and 36 is 36.
What is the HCF of 25 and 37?
The highest common factor (HCF) of 25 and 37 is 1. HCF is the largest positive number that divides two given numbers without leaving any remainder. To find the HCF of two numbers, use the Prime Factorization Method.
This method involves breaking down each of the two numbers into its prime factors.
The prime factors of 25: 25 = 5 x 5
The prime factors of 37: 37 = 37
The common factors of 25 and 37 are 1. Hence, the highest common factor (HCF) of 25 and 37 is 1.
How do you solve HCF short tricks?
The most effective way to solve HCF (or Highest Common Factor) short tricks is by using a method known as the “Euclidean Algorithm.” This method is based on the observation that if two numbers a and b are both divisible by the same number, then their GCD (or greatest common divisor) is that number.
To use the Euclidean Algorithm, the following steps should be taken:
1. Start with two given numbers a and b.
2. Find the remainder when a is divided by b.
3. Divide b by the remainder and store the result in a new variable c.
4. If the result c is 0, then the GCD is b.
5. If the result c is not 0, then divide a by c and store the result in a new variable d.
6. Repeat steps 3-5 until the result is 0, and the last non-zero result will be the GCD.
By using the Euclidean Algorithm, short tricks can be solved quickly and easily. Additionally, the Euclidean Algorithm is widely used to solve many other types of mathematics problems.
What is the fastest way to find the HCF of 3 numbers?
The fastest way to find the Highest Common Factor (HCF) of three numbers is to first list out all the prime factors of each number. Then, you can use a Venn diagram to highlight the common factors between the three numbers.
The intersection of the prime factors are those that are shared amongst all three numbers and make up the HCF. For example, if the numbers are 12, 15, and 18; the prime factors would be 2, 3, and 2, 3, and 3.
Looking at the Venn diagram, the common factors are 3, which makes up the HCF.
What is an example of HCF of three numbers?
An example of the Highest Common Factor (HCF) of three numbers is 24. To calculate the HCF, you would need to break down each number into its prime factors and find the highest common factors based off of the prime factors.
For example:
Number 1: 48
Prime factors: 2 x 2 x 2 x 2 x 3
Number 2: 36
Prime factors: 2 x 2 x 3 x 3
Number 3: 12
Prime factors: 2 x 2 x 3
The highest common factor of these three numbers would be 2 x 2 x 3 = 24, which is the HCF of 48, 36, and 12.
