0-2 The sum of two.consecutive number which was
divisible by 7 are 343 then and find the both
consecutive numbers
Answers
Answer:
Natural Numbers: The numbers 1,2,3,4.... are called natural numbers or positive integers.
Whole Numbers: The numbers 0,1,2,3.... are called whole numbers. Whole numbers include “0”.
Integers: The numbers .... -3, -2, -1, 0, 1, 2, 3,.... are called integers. You will see questions on integers in almost all the exams where you see number system aptitude questions.
Negative Integers: The numbers -1, -2, -3, ... are called negative integers.
Positive Fractions: The numbers(2/3) ,(4/5) ,(7/8) ... are called positive fractions.
Negative Fractions: The numbers -(6/8) ,-(7/19) , -(12/17) ... are called negative fractions.
Rational Numbers: Any number which is a positive or negative integer or fraction, or zero is called a rational number. A rational number is one which can be expressed in the following format ⇒(a/b) , where b ≠ 0 and a & b are positive or negative integers.
Irrational Numbers: An infinite non-recurring decimal number is known as an irrational number. These numbers cannot be expressed in the form of a proper fraction a/b where b ≠ 0. e.g.√2 , √5 , Π, etc.
Surds: Any root of a number, which cannot be exactly found is called a surd. Essentially, all surds are irrational numbers. e.g. √2 , √5 etc.
Even Numbers: The integers which are divisible by 2 are called even numbers e.g. -4, 0, 2, 16 etc.
Odd Numbers: The integers which are not divisible by 2 are odd numbers e.g. -7, -15, 5, 9 etc.
Prime Numbers: Those numbers, which are divisible only by themselves and 1, are called prime numbers. In other words, a number, which has only two factors, 1 and itself, is called a prime number. e.g. 2, 3, 5, 7, etc.
Note: 2 is the only even prime number.
There are 25 prime numbers upto 100. These are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 & 97. These should be learnt by heart.
Co-Prime Numbers: Two numbers are considered to be prime to each other if their HCF is 1. e.g. 5 and 24 are prime to each other. In other words, 5 and 24 are co-prime.
To check whether a number is prime, e.g. 79, we do not need to check all the factors below 79. The square of 8 is 64 & that of 9 is 81. Therefore, check if any of the prime numbers less than 9 is a factor of 79. The prime numbers 2, 3, 5, 7 are not the factors of 79. So, 79 is a prime number.
Composite Number: A number, which has factors other than itself and 1, is called a composite number. e.g. 9, 16, 25....
Note: 1 is neither a composite number nor a prime number.
Illustration: Which of the following is a prime number?
1. 31
2. 91
3. 87
4. 57
Sol: Here 91 is divisible by 7, so 91 is not a prime number. 87 is divisible by 3. So it is also not a prime number. 57 is not a prime number as it is divisible by 3. 31 has only two factors 1 and 31, so it is a prime number.
Consecutive Numbers: Numbers arranged in increasing order and differing by 1 are called consecutive numbers. e.g. 4, 5, 6, 7 etc.
Real Numbers: The natural numbers, integers, whole numbers, rational numbers and irrational numbers constitute the set of real numbers. Every real number can be represented by a point on a number line.
Perfect Numbers: If the sum of all the factors of a number excluding the number itself happens to be equal to the number, then the number is called as perfect number. 6 is the first perfect number. The factors of 6 are 1, 2, 3 & 6. Leaving 6 the sum of other factors of 6 are equal to 6. The next three perfect numbers after 6 are: 28,496 and 8128.
Complex Numbers: Complex numbers have a real and an imaginary component; e.g. (√-2 - 4), (2 +√-3 ), etc. Square root of any negative number is an imaginary number - e.g.√-2 ,√-3 . The square root of a negative number does not exist in the real sense. Such numbers are called imaginary numbers.
Fibonacci Numbers: The numbers, which follow the following series are known as Fibonacci numbers. E.g. 1,1,2,3,5,8,13,21..... The series is obtained by adding the sum of the preceding two numbers. In general for a Fibonacci number X, Xi+2 = Xi+1 + Xi.