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FACTOR AND MULTIPLE FACTOR If a number is exactly divisible by another number, then the second number is called the FACTOR of the first number. Ex: 4 is divisible by 2, then 2 is called FACTOR of 4. So, a FACTOR of a number is an exact divisor of that number. Ex: 1,2,3 and 6 are exact divisors of 6. So, 1,2,3 and 6 are factors of 6. But 4 and 5 are not the FACTORS of 6. MULTIPLE A MULTIPLE of a number is a number obtained by multiplying it by a natural number. Ex: 3, 6, 9, 12, 15, 18, …….. are MULTIPLES of 3. So, if a number is a factor of another number, then the bigger number is called the MULTIPLE of the smaller number. Ex: If 2 is a factor of 4, then 4 is MULTIPLE of 2. PROPERTIES FACTOR MULTIPLE Factors of a given number are finite. Multiples of a given number are infinite. 1 is a factor of every number. 1 is not a multiple of every number. Every number is a factor of itself. Every number is a multiple of itself. The greatest factor of a number is that The lowest multiple of a number is that number itself. number itself. Every factor of a number is an exact divisor of Every number is a multiple of each of its that number. factor. Every factor of a number is less than or equal Every multiple of a number is greater than or to that number. equal to that number MySubjectTutor.com Page 1 HIGHEST COMMON FACTOR (HCF) The HCF of two or more numbers is the largest number that devides all the given numbers. Ex: HCF of 24 and 36 Factors of 24 – 1, 2, 3, 4, 6, 8, 12 and 24 Factors of 36 – 1, 2, 3, 4, 6, 9, 12 and 36 Now Common Factors – 1, 2, 3, 4, 6 and 12 So, Highest Common Factor is 12. Trick: 2 24, 36 2 12, 18 3 6, 9 2, 3 So, HCF of 24 and 36 = 2x2x3 = 12 (Multiplication of extreme left numbers) LEAST COMMON MULTIPLE (LCM) The LCM of two or more numbers is the smallest number which is divisible by all the given numbers. Ex: LCM of 8 and 12 Multiples of 8 – 8, 16, 24, 32, 40, 48, 56, 64, 72, ………….. Multiples of 12 – 12, 24, 36, 48, 60, 72, ……………. No Common Multiples are 24, 48, 72, ……………… So, Lowest Common Multiple is 24. Trick: 2 8, 12 2 4, 6 2, 3 So, LCM of 8 and 12 = 2x2x2x3 = 24 (Multiplication of extreme left and bottom numbers.) MySubjectTutor.com Page 2 Note: The product of HCF and LCM of two numbers (Not more than two numbers) is equal to the product of those numbers. The HCF of any two prime or co-prime numbers is equal to 1. The LCM of any two prime or co-prime numbers is equal to their product. The HCF of two or more numbers is never greater than any of those numbers. The LCM of two or more numbers is never less than any of those numbers. The HCF of two or more numbers is a factor of their LCM. If m is a factor of n, then HCF of m and n is m and LCM of m and n is n. *** MySubjectTutor.com Page 3