Page 173 - Demo

172 Arrow-Puffin-4_Semester-1 MathsHIGHEST COMMON FACTOR (BY FACTOR METHOD)The highest common factor (HCF) is the greatest number, which divides two or more numbers without a remainder.The highest common factor is also called the greatest common divisor (GCD).Consider two numbers 6 and 8.Factors of 6 : 1 2 3 6 Factors 8 : 1 2 4 8Common factors of 6 and 8 are 1 and 2.The highest common factor of 6 and 8 is 2.Example 1 : Find the highest common factor of 8, 12 and 16.Factors of 8 : 1 2 4 8Factors of 12 : 1 2 3 4 6 12Factors of 16 : 1 2 4 8 16 Common factors of 8, 12 and 16 are 1, 2 and 4The highest common factor of 8, 12 and 16 is 4.Note : If a number is a factor of another number, then their HCF is the smaller of the two numbers.Example 2 : Find the highest common factor of 6 and 18. (6 is a factor of 18)Factors of 6 : 1 2 3 6 Factors of 18 : 1 2 3 6 9 18Common factors of 6 and 18 are 1 2 3 6Highest common factor of 6 and 18 is 6. Example 2 : Write the common factors of 20 and 25.Factors of 20 : 1 2 4 5 10 20Factors of 25 : 1 5 25Common factors of 20 and 25 are 1 and 5.Example 3 : Write the common factors of 16, 24, 60 and 64.Factors of 16 : 1 2 4 8 16Factors of 24 : 1 2 3 4 6 8 12 24Factors of 60 : 1 2 3 4 5 6 10 12 15 20 30 60Factors of 64 = 1 2 4 8 16 32 64Common factors of 16, 24, 60 and 64 are 1, 2 and 4.Let's Understand Conceptual Understanding