Elementary Number Theory MCQ

Which of the following is a false statement ? 1. Any two-prime numbers are always relatively prime to each other 2. Two relatively prime numbers need not be prime numbers 3. The G.C.D of two relatively prime numbers is 1 and their LCM is the product of those numbers 4. If a/bc, then a/b and a/c for any three natural numbers a,b,c

If X = 2xpx5xq=rx3xsx7, where p, q, r, s are distinct primes, then p+q+r+s= ….. 1. 15 2.17 3.7 4.10

Unique factorisation theorem is also called as : 1. Fundamental theorem in Arithmetic 2. Fundamental theorem in Algebra 3. Fundamental theorem in Geometry 4. Fundamental theorem in Calculus

The property which is not obeyed by the relation is a factor of is : 1. reflexive 2. symmetric 3. transitive 4. antisymmetric

Which of the following pairs of numbers do not have their product as LCM? 1. Any two prime numbers 2. Any two relatively prime numbers 3. 1 and any natural numbers 4. Any two natural numbers

If the L.C.M. of 324 and 360 is 3,240 then their G.C.D. is : 1. 180 2.72 3.36 4.18

If the product of two numbers is 6912 and their LCM is 288, then their G.C.D. is : 1.48 2.12 3.24 4.36

The G.C.D. and L.C.M. of two numbers are 12 and 72. If one of them is 36, then the second number, is 1. 18 2.24 3.72 4.36

The least natural number which when divided by 18, 24 and 30 leaves the remainder 14, 20, 26 respectively, is 1. 354 2.360 3.364 4.356

The least natural number which leaves no remainder when divided by 1, 2, 3, ..... 10, is 1.55 2.2250 3. 2520 4. 2025

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