# Number System in Mathematics

Types of Numbers in Maths

Natural Numbers:--
Natural numbers are the set of positive integers from 1 to infinity. The set of natural numbers is represented by the letter “N”. For example 1, 2, 3, 67, 89 all are natural number

Whole Numbers:--
Set of natural number including 0 is called Whole Numbers. For example 0, 1, 2, 3, 67, 89 all are Whole number

Composite Numbers:--
A composite number is a natural number or a positive integer which has more than two factors. For example, 16 has factors like 1, 2, 4, 8, 16

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### Related FAQs

Q. The sum of the digits of a 2-digit number is 11. If we add 45 to the number, the new number obtained is a number formed by interchange of the digits. What is the number?

Ans: Let x is the first digit of number and second digit of number is y. So the number is 10*x + y As it is given that sum of digits is 11 So x + y = 11  And it is also given that if we add 45 t... read more

Q. Among three numbers, the first is twice the second and thrice the third, if the average of three numbers is 517, then what is the difference between the first and the third number?

Ans: Let first number is = a So second number is = a/2 and third number is = a/3 As the average of three numbers is 517 So (a + a/2 + a/3) / 3 = 517 a + a/2 + a/3 = 3*517 11a/6 = 3*517 11a/6 = 155... read more

Q. If the fractions 1/2, 2/3, 5/9, 6/13, and 7/9 are arranged in ascending order of their values, which one will be the fourth?

Ans: convert the numbers to their decimal form as 1/2 = 0.50, 2/3 = 0.67, 5/9 = 0.56, 6/13 = 0.56, 7/9 = 0.78  Now arranged in ascending order as 0.46. 0.50. 0.56, 0.67, 0.78 So the fourth decimal ... read more

Q. The product of two natural numbers is 9222. If they differ by 19 then find out the sum of the number.

Ans: Let a and b are two natural number where (a > b).  It is given that product of two natural number is 9222 Therefore a*b = 9222  and a - b = 19 b(b+19) = 9222,  b2 + ... read more

Q. What is the sum of all natural numbers between 100 and 200 which are multiples of 3?

Ans: Between 100 to 200,  First natural number And Last natural number which is multiple of 3  is 102 and 198 So first natural number a = 102 Last natural number = 198 So Total number are b/w ... read more

Q. If the sum of 1st 11 terms of an A.P is equal to sum of 1st 19 terms of that A.P then, Find the sum of 1st 30 terms?

Ans: Sum of first 11 terms of an AP equals the sum of first 19 terms of that AP. Therefore  S11 = (11/2)[2a + 10d] ........(1)                   S19... read more

Q. A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is _________.

Ans: Divisor = 555 + 445 = 1000 Quotient = 2×(555 − 445) = 220 Remainder = 30 As Dividend = Divisor×Quotient + Remainder                  ... read more

Q. The least number which must be added to 1728 to make it a perfect square is

Ans: Square of 42 is = 1764 Square of 41 is = 1681 So the nearest perfect square number from 1728 is 1764,  because this is nearest to 1728 So, the least number which must be added to 1728 to make ... read more

Q. In a zoo there are rabbits and pigeons. If their heads are counted, they are 90 while their legs are 224. Find the number of pigeons in the zoo?

Ans: Let the number of rabbits in the zoo is = R Total no of heads = 90  So no of pigeons in the zoo is = 90 - R As we know pigeon has 2 legs and a rabbit has 4 legs  Total legs are 224 So &... read more

Q. If x^2 + mx – 30 = (x – 5) (x + 6) then m =

Ans: x2 + mx - 30 = (x – 5) (x + 6) x2 + mx - 30 = x2 + 6x - 5x - 30 x2 + mx - 30 = x2 + x - 30 x2 + mx - 30 - x2  - x + 30 = 0 mx - x = 0 x(m - 1)... read more

Q. Give possible expression for the length and breadth of the rectangle having area x^2 – 14x + 40

Ans: It is given that Area of the rectangle = x^2 - 14x + 40 Factorising the given polynomial - x2 - 14x + 40 x2 - 10x - 4x + 40 x(x - 10 ) - 4(x - 10) (x - 10) (x - 4) ANSWER : The ... read more

Q. The zero(s) of the polynomial x^2 – 8 is (are) :-

Ans: As x2 – 8 = 0    x2 = 8    x = √8    x = √4*2    x = 2√2 Hence answer is 2√2... read more

Q. When a number is subtracted from the number 8,12 and 20, the remainders are in continued proportion, Find the number ?

Ans: Given numbers are 8,12 and 20 Let x be the subtracted number As remainders are in continued proportion So :-- (8-x) / (12 –x) = (12-x) / (20 –x) (8-x)(20-x) = (12 – x)(12 –... read more

Q. If 1/6 th of wall is painted blue, 1/3rd is painted yellow and remaining 9m is painted white, what is the length of the wall?

Ans: Let assume that the total length of the wall is x As 1/6 th of wall is painted by blue color So wall painted by blue color = x/6 As 1/3 rd of wall is painted by yellow color So wall painted by yel... read more

Q. What is the unit digit of the sum of first 131 whole numbers?

Ans: In case of first 131 whole numbers , 0 is the first number and 130 is the last number so here the sum will be 0 + 1 + 2 + ---------------------------- + 130 0 + (1 + 2 + ----------------------------... read more

Q. If HCF of 65 and 117 is expressible in the form 65m – 117, then find the value of m.

Ans: Fist we calculate the Hcf of 65 and 117 65 = 13 X 5 117 = 13 X 3 X 3  S0 H.C.F. of 65 and 117 is 13  Now according to the question  65m -117 = 13  65m = 13 + 117  ... read more

Q. Show that any positive even integer is of the form 6m or 6m + 2 or 6m + 4,where m is some integer

Ans: Let n be the given positive even integer. Lets assume that on dividing n by 6, m be the quotient and r be the remainder. Now according to Euclid's division lemma, we have n = 6m + r, whe... read more

Q. The larger of two supplementary angles exceeds the smaller by 24 degree. Find the angles

Ans: Let the two angle be x and y Where x is the larger angle and y is the smaller angle Now according to given condition- x + y = 180 ---------(1) x - y = 24 -----(2) Now from eq-2  x = 24 + y... read more

Q. Using prime factorization, find HCF and LCM of 168 and 448.

Ans: By using prime factorisation. Prime factorisation of 168  =  2 x 2 x 2 x 7 x 3 Prime factorisation of 448  =  2 x 2 x 2 x 2 x 2 x 2 x 7 So, the HCF of 168, 448    =&nb... read more

Q. What are the composite numbers between 61 to 65?

Ans: A composite number is a natural number or a positive integer which has more than two factors. For example, 16 has factors like 1, 2, 4, 8, 16 So between 61 and 65 below are the composite numbers ... read more

Q. Find the HCF of the first 3 composite numbers

Ans: A composite number is a natural number or a positive integer which has more than two factors. For example, 12 has factors like 1, 2, 3, 4, 6 So first 3 composite numbers are 4, 6, 8 Now factoriz... read more

Q. Write 3/4 as a decimal OR What is the decimal form of 3/4 ?

Ans: As 3/4 = (3/4)x(25/25)        = 75/100        = 0.75 Hence 0.75 is the decimal form of 3/4.... read more

Q. Write down the smallest prime number. Or which is the smallest prime number?

Ans: The number which can not be divided by any number excluding 1 and itself is called prime number. one is the smallest prime number.... read more

Q. Write down a common factor of 16 and 72 that is greater than 2.

Ans: Factors of 16 and 72 16 = 1 x 2 x 2 x 2 x 2 72 = 1 x 2 x 2 x 2 x 3 x 3 Common factor of 16 and 72 is 1 x 2 x 2 x 2 = 8 Common factor of 16 and 72 that is greater than 2 is 8... read more