# Mathematics - Class 6 / Grade 6

- Playing With Numbers (The Highest Common Factor (HCF)/ Greatest Common Divisor (GCD))
### Playing With Numbers (The Highest Common Factor (HCF)/ Greatest Common Divisor (GCD))

Math - Class 6 - Playing With Numbers (The Highest Common Factor (HCF)/ Greatest Common Divisor (GCD)) - Key Points/Notes/Worksheets/Explanation/Lesson Tags: Greatest Common Divisor (GCD) for sixth class, Highest Common Factor (HCF) for 6th standard, Find HCF of 18 and 48. HCF with Prime Factorization Method, Find the HCF of 30 and 42. HCF by Division Method for grade VI, Steps to find HCF with prime factorization method for class 6, Steps to find HCF by division method, Steps to find HCF by long division method. How to find the highest common factor? How do we find the greatest common factor? What is the highest common factor of 70, 105 and 175? Method of H.C.F. Examples of HCF, Worksheets PDF on HCF, HCF worksheets and practice pages, What is HCF? Definition of HCF, HCF of any two consecutive numbers is 1. HCF of two consecutive even numbers is 2. HCF of two consecutive odd numbers is 1. HCF of two prime numbers is 1. HCF of an even number and an odd number is 1.### Highest Common Factor

The Highest Common Factor (HCF) of two or more given numbers is the

__highest (or greatest) of their common factors__. It is also known as Greatest Common Divisor (GCD).Example: Find HCF of 18 and 48

We can find HCF of 18 and 48 by finding the highest common factors of 18 and 48.

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors of 18 and 48 = 1, 2, 3, 6 (6 is the highest of these common factors)

HCF = 6

**HCF with Prime Factorization Method**HCF of numbers can also be found by prime factorization of the numbers.

__Example:__Find the HCF of 30 and 42.

Prime factors of 30 = 2 x 3 x 5

Prime factors of 42 = 2 x 3 x 7

Common factor of 30 and 42 = 2 x 3 = 6

Therefore, Highest common factor (H.C.F) of 30 and 42 = 56

**HCF by Division Method**Step1: Divide the two given numbers together by their common prime factors.

Step2: Stop dividing when there is no common prime factor left.

Step3: Multiply the common prime factors to find the HCF.

__Example 1:__Find the HCF of 70, 105 and 175.5

70, 105, 175

7

14, 21, 35

2, 3, 5

Now we cannot divide further with common factor.

Multiply common factor to get HCF = 5 x 7 = 35

So, HCF of 70, 105 and 175 = 35

__Example 2:__Find the HCF of 91, 112 and 49.7

91, 112, 49

13, 16, 7

Now we cannot divide further with common factor.

Multiply common factor to get HCF = 7

So, HCF of 91, 112 and 49 = 7

**HCF by Long Division Method**The method of long division is more useful for large numbers.

**Step1:**Identify the larger number from the given two numbers and divide the larger number by the smaller number.**Step2:**Now remainder become divisor and the previous divisor become the dividend. Divide the new dividend with new divisor.**Step3:**Continue this process till we get remainder as 0.**Step4:**The last divisor in this process is the H.C.F of the two numbers__Example:__Find HCF of 27 and 63

**Explanation****Step1:**Start dividing 63 by 27**Step2:**Now, remainder 9 becomes the divisor and previous divisor 27 has become the dividend. Divide 27 by 9.**Step 3:**Now remainder is 0. So, further division is not possible and the last divisor 9 becomes the HCF of 27 and 63.

**Note:**1. HCF of any two consecutive numbers is 1.

2. HCF of two consecutive even numbers is 2.

3. HCF of two consecutive odd numbers is 1.

4. HCF of two prime numbers is 1.

5. HCF of an even number and an odd number is 1.

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