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**1.4 THE NUMBER TREE**

**1.5 ODD AND EVEN NUMBERS**

This is a property of Integers. But since our questions are limited to the Whole numbers, we will keep our studies limited to them.

By Definition **Even ****Numbers **are those which are divisible by 2. They are the numbers with their unit digit as either 2, 4, 6, 8 or 0. The general expression of Even numbers is 2n where n is a whole number.

By Definition **Odd ****Numbers **are those which are not divisible by 2. They are the numbers with their unit digit as either 1, 3, 5, 7 or 9. The general expression of Odd numbers is 2n+1 where n is a whole number.

__Certain Operations on Whole Numbers__:**(i)** Odd Â± Odd = Even**(ii)** Even Â± Even = Even**(iii)** Odd Â± Even = Odd**(iv)** Even Â± Even Â± Even ........... n terms = Even**(v)** Odd Â± Odd Â± Odd .............. n terms = Even if n is Even, Odd if n is Odd**(vi)** Odd Ã— Odd = Odd**(vii) **Even Ã— Odd = Even**(viii) **Even Ã— Even = Even**(ix) **Even Ã— Even Ã— Even ....... n terms = Even**(x) **Odd Ã— Odd Ã— Odd ....... n terms = Odd**(xi)** (Even)^{n} = Even**(xii)** (odd)^{n} = Odd

Question 1:If a is even what would 5a + 1 be

Question 2:If a is even and b is odd what would a^{3} + 3b + 6 be

Question 3:If 5a - 2 is even what would a be

**1.6 PRIME AND COMPOSITE NUMBERS**

Being Prime is a property of Natural Numbers. All those numbers which are divisible by exactly 2 numbers i.e. itself and unity "1".**Example:** 2, 3, 5, 7, 11 etc.

**Composite **are the numbers which are divisible by more than 2 numbers i.e. itself, unity "1" and at least one other.**Example:** 4, 6, 8, 9, 10 etc.

1 is neither Prime nor Composite.

Question 4:How many Prime numbers are there less than 100

Question 5:Which of the following cannot be the sum of two prime numbers.

Question 6:State Whether True or False

All Prime numbers are Odd

Question 7:State Whether True or False

Sum of Any 2 prime numbers is always Even

Question 8:State Whether True or False

Product of Any two prime numbers is always Odd

Question 9:State Whether True or False

There are no 4 digit Prime numbers.

**Property of Prime Numbers:**

All Prime numbers greater than 3 are of the form 6n Â± 1 but not all numbers of the form 6n Â± 1 are Prime. This property means when prime numbers greater than 3 are divided by 6 they leave a remainder of 1 or 5.

Question 10:Which of the following is a prime numbers.

**1.7 CO - PRIME NUMBERS**

This is a property of a pair or more than two natural numbers. Two numbers are said to be co-prime if the only number which can completely divide both the numbers is 1. No number other than 1 can divide both the given numbers of the pair. These numbers in themselves can be prime or composite. 1 is co-prime with all the natural numbers other than 1.**Example:** (3, 7); (4, 15); (3, 10) etc.

A set of numbers is said to be co-prime if their HCF is 1. We will be learning about HCF in the following chapters.**Example:** (3, 7, 11); (4, 15, 10); (3, 10, 8) etc.

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81 videos|93 docs|110 tests

### Practice Questions for Number Systems Part-1

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### Practice Questions for Number Systems Part-2

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### Practice Questions for Number Systems Part-3

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### Practice Test: Number System (Level 1)

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### Practice Test: Number System (Level 2)

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