# Question Bank - Number theory

• Number of Questions - 37
Topic - Number Theory
Answer Key available ? - No

• Q1) For the number 2^3 * 3^2 * 5^4, find the number of

1. Even factors
2. odd factors
3. Composite factors

• Q2) Find the Product and Sum of all factors of 2^3 * 3^2 * 5^4

• Q3) How many factors of 2^3 * 3^2 * 5^4 are multiples of 5 ?

• Q4) Number of ways in which 2^3 * 3^2 * 5^4 be resolved into product of 2 co-primes (a,b,) ?

• Q5) How many factors of 2^3 * 3^2 * 5^4 are less than and co-prime to it ? Also, find the sum of all those factors.

• Q6) In how many ways can 2^3 * 3^2 * 5^4 be written as SUM of consecutive natural numbers and as SUM of consecutive integers ?

• Q7) How many pairs exist which have LCM = 2^3 * 3^2 * 5^4 ?

• Q8) How many triplets exist which have LCM = 2^3 * 3^2 * 5^4 ?

• Q9) How many Factor triplets (a,b,c) of 2^3 * 3^2 * 5^4 exist which have HCF = 1

• Q10) Number of ways in which 2^3 * 3^2 * 5^4 can be resolved into product of 3 co-primes? Also, find the number of ways the 2^3 * 3^2 * 5^4 can be written as the SUM of 2 co-primes.

• Q11) Find the sum of all 4 digit numbers such that its Thousands digit Tens digit and Units digits are in ratio 2:3 :1 and hundredth digit is equal to units digit ?

• Q12) Out of first 20 natural numbers , how many 3 element subsets can be formed such that the product of 3 elements is divisible by 4 ?

• Q13) How many ways can 720 be expressed as Product of 2 co primes

• Q14) If 1/a + 1/b + 1/c + 1/d = 2, where a , b , c , d are distinct natural numbers. what is the value of a + b + c + d ?

• Q15) If (1+2^x) is a divisor of 1 + 2 + 2^2 +2^3 +2^4 +........+ 2^255 then what is the max value of "x" possible ?

• Q16) How many distinct digits are there in the largest 12 digit perfect square ?

• See there is a pattern the series of Squares of 9's
9^2 = 81
99^2 = 9801
999^2 = 998001
9999^2 = 99980001
Like wise 12 digit is 999998000001 which is 999999^2
this is pattern . i hope u r able to relate to this ..
so how many distinct digits are there in 999998000001 ??
its 4

• Q17) How many distinct pair of factors of 21000 have HCF as 75 ?

• Q18) The HCF of x, y and z is 8 and the LCM of x,y, z is a 4 digit number .. if x-y = y-z= 8 .. find the maximum possible value of z

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