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- Ex : 6 and 7 are Factors of 42.
- Multiple : A number is said to be a multiple of another, when it is Exactly divisible by the other
- Ex : 42 is a multiple of 6 and 7
- Prime Number : Prime number is a number which has no factors except itself and Unity.
- Ex :2, 3, 5, 7, 11, 13, 17 etc are prime numbers
- Composite Number : Composite number is a number which has other factors besides itself and Unity.
- Ex : 14, 15, 16, 18 etc
- Co-Prime : Two numbers are said to be Co-Prime (Prime-To-Each Other) when they have no common factors except Unity.
- Note : The Co-Primes need not necessarily be Primes.
- 15 and 19
- 15, 17 and 22 are Co-Primes
- Common Multiple : A Common Multiple of two or more numbers is a number which is exactly divisible by each of them.
- Ex : 12 is a common multiple of 2, 3, 4 and 6
- Least Common Multiple (LCM) : The LCM of two or more given numbers is the Least Number which is exactly divisible by each of them.
- Ex :
- 20 is the Common Multiple of 2, 4, 5 and 10
- 40 is the Common Multiple of 2, 4, 5 and 10
- 80 is the Common Multiple of 2, 4, 5 and 10, But
- Here 20 is the Least Common Multiple of 2, 4, 5, and 10
- Highest Common Factor (HCF) : The HCF of two or more numbers is the Greatest Number which divides each of them Exactly.
- It is also Called Greatest Common Divisor (GCD)
- Ex : Find the HCF of 18, 24
- Factors of 18 --> 1, 2, 3, 6, 9, 18
- Factors of 24 --> 1, 2, 3, 4, 6, 8, 12, 24
- Here the Greatest number, which divides them exactly is 6. So 6 is the H.C.F of 18, 24
- HCF by factorization :
- Express each of the given number as the product of Prime Factors
- Choose common factors
- Find the Product of Lowest Power of these Factors.
- This Product is the required HCF of the given Numbers
- HCF by Method of Division :
- Consider two different numbers.
- Divide the longer number by the smaller one.
- Now divide the divisor by the reminder.
- Repeat this process of dividing the preceding divisor by the last reminder obtained, till you get the reminder "0"
- The LAST DIVISOR is the HCF of the given TWO numbers