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

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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

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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

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

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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

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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

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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

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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

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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

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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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