PE 3 - Numbers | Algebra - Number Theory
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For how many of the first 200 odd natural numbers is the total number of factors even?
Solution
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ReportIn how many ways can 97 be expressed as the sum of two natural numbers that are coprime to each other?
How many three-digit natural numbers are there such that unit’s digit of each of which is always less than tens as well as hundreds digit?
How many natural numbers below 1000 are divisible by at least one of 2, 3, 4, 6, 8 and 10?
A natural number N which is not a perfect cube, has exactly four factors. The sum of the positive factors of N that are less than N is 202. Find the value of N.
If x = 175 + 174 + 17 + 1 and y = 118 – 115 – 113 – 1, then which of the following statements is true?
- (a)
x and y are both prime
- (b)
x is prime but y is composite
- (c)
y is prime but x is composite
- (d)
x and y are both composite
If p is a prime number greater than 3, (p2 – 1) is divisible by which of the following?
- (a)
36
- (b)
24
- (c)
18
- (d)
All of these
A denotes the set of all the prime numbers less than 100. How many zeroes does the product of the elements of A end with?
The difference of a four-digit number and any number formed by permuting its digits would always be divisible by
- (a)
18
- (b)
11
- (c)
10
- (d)
9