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Elementary Number Theory MCQ. We covered all the MCQs on number theory with answers in this post so that you can practice well for the exam for free.
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Practice Bits of Elementary Number Theory for Students
The G.C.D. of (2x3x3), (2×2×2×2× 3), is :
1.2×2×3
2. 2x2x2x2
3.3×3
4.2x2x2x2x3x3
Option 1 – 2×2×3
The G.C.D. of (2 x 2 x 2 x 3), (2 x 3 x 5), (2 × 3 × 7), is :
1. (2 × 3)
2. (2x2x2x3)
3. (2×3×5)
4. (2×3×7)
Option 1 – (2 × 3)
The largest number which divides the numbers 400 and 852 and leaves the remainders 4 and 5 respectively are :
1. 11
2. 15
3.16
4.9
Option 1 – 11
The number which when divided by 4 gives the quotient 5 and remainder 2, is
1.20
2.18
3.22
4.24
Option 3 – 22
If the G.C.D of two numbers is 18 and the first 4 quotients obtained in the division are 2,1,2,2 then the numbers are:
1. 126,342
2. 125,345
3. 120,342
4. 122,344
Option 1 – 126,342
If the G.C.D of two numbers is 7 and the first 3 quotients are 1,2,3 then the sum of the two numbers, is:
1. 120
2. 119
3. 118
4. 121
Option 2 – 119
If X= pxpxpxqxq and Y = pxpxqxr, where p, q and r are distinct primes, then the LCM of X, Y is
1. pxpxqxpxqxr
2. pxpxq
3. pxpxpxqxq
4. pxpxqxr
Option 1 – pxpxqxpxqxr
The least natural number which when divided by 10 leaves the remainder 5 and when divided by 20 leaves the remainder 15 and when divided by 30 leaves the remainder 25, is :
1.60
2.55
3.65
4.50
Option 2 – 55
The least natural number which when divide by 2, 3, 4, 5 or 6 leaves the remainder 1, is :
1. 61
2.59
3. 121
4.62
Option 3 – 121
The least natural number which leaves no remainder when divided by 1, 2, 3, ….. 10, is
1.55
2.2250
3. 2520
4. 2025
Option 3 – 2520
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
Option 4 – 356
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
Option 2 – 24
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
Option 3 – 24
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
Option 3 – 36
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
Option 4 – Any two natural numbers
The property which is not obeyed by the relation is a factor of is :
1. reflexive
2. symmetric
3. transitive
4. antisymmetric
Option 2 – symmetric
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
Option 1 – Fundamental theorem in Arithmetic
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
Option 2 – 17
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
Option 4 – If a/bc, then a/b and a/c for any three natural numbers a,b,c
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