**LCM AND HCF OF WHOLE NUMBERS**

CONTENT
- Rules of Divisibility
- Definitions: Even, Odd, Prime and Composite Numbers
- Factors, Multiples and Index Form
- Expressing Numbers as Product of Prime Factors
- Common Factors and the Highest Common Factor (H.C.F) of Whole Numbers
- Least Common Multiple (L.C.M) of Whole Numbers
- Quantitative Reasoning on LCM and HCF

**Rules of Divisibility**

There are some simple rules of divisibility which enable us to find out whether a certain number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11.
Any whole number is exactly divisible by | ||

2 if its last digit is even or 0 | ||

3 if the sum of its digits is divisible by 3 | ||

4 if its last two digits form a number divisible by 4 | ||

5 if its last digits is 5 or 0 | ||

6 if its last digit is even and the sum of its digits is divisible by 3 | ||

8 if its last three digits form a number divisible by 8 | ||

9 if the sum of its digits is divisible by 9 | ||

10 if its last digit is 0 | ||

11 if the difference between the sum of the digits in the odd places and the sum of the digits in the even places is divisible by 11, or the difference is 0. | ||

**CLASS ACTIVITY**1. Using the rules of divisibility, find out which of the following numbers are divisible by (a) 2 (b) 5 (c) 4 (i) 136 (ii) 4 881 (iii) 372 (iv) 62, 784 (v) 1010 2. Which of the following numbers are divisible by (a) 3 and 9 (b) 4 and 5? (i) 637 245 (ii) 134 721 (iii) 10140.

**Definitions**

**Even Numbers:**Even numbers are numbers that when divided by two has no remainder. All numbers that end in 0, 2, 4, 6, and 8 are even. Examples include: 34, 86, 26890, etc.

**Odd Numbers:**These set of numbers has a remainder of one when it is divided by 2. All numbers that end in 1, 3, 5, 7 and 9 are odd numbers. Examples are 81, 1247, 30096, etc.

**Composite Numbers:**These are numbers that are not prime numbers. They have factors other than 1 and the number itself. All even numbers except 2 are composite numbers.

**Factors, Multiples and their Relationship**

**Factors:**When two or more smaller numbers multiply to give a bigger number, these smaller numbers are called

**factors**of the bigger number

**.**In another sense we can say a factor is a number which can divide another number exactly without any remainder. Examples:

- The factors of 24 are 1, 2, 3, 4 , 6 , 8 , 12 , and 24.
- The factors of
- The factors of 50 are 1, 2, 5, 10, 25 and 50.

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