250+ TOP MCQs on Number Theory – Highest Common Factors

Discrete Mathematics Questions and Answers for Campus interviews on “Number Theory – Highest Common Factors”.

1. A Highest Common Factor of a, b is defined as ___________
a) It is the smallest integer divisible by both a and b
b) It is the greatest integer divisor of both a and b
c) It is the sum of the number a and b
d) None of the mentioned

Answer: b
Clarification: Defination of HCF(a, b)-greatest integer divisor of both a and b.

2. The HCF of two number 1, b(integer) are _________
a) b + 2
b) 1
c) b
d) None of the mentioned

Answer: b
Clarification: Since 1 is the greatest integer divisor of both 1 and b.

3. If a,b are integers such that a > b then hcf(a, b) lies in _________
a) a> hcf(a, b)>b
b) a>b> = hcf(a, b)
c) hcf(a, b)> = a>b
d) None of the mentioned

Answer: b
Clarification: Hcf of number is either equal to smallest number or is least among all.

4. HCF of 6, 10 is?
a) 60
b) 30
c) 10
d) 2

Answer: d
Clarification: Since 2 is the greatest integer divisor of both 6 and 10.

5. The product of two numbers are 12 and there LCM is 6 then HCF is?
a) 12
b) 2
c) 6
d) None of the mentioned

Answer: b
Clarification: The hcf of two number a and b is given by
(hcf(a, b)) = ab/ lcm(a, b).

6. If LCM of two number is 10 and GCD is 5 then the product of two numbers is?
a) 45
b) 50
c) 7
d) 49

Answer: b
Clarification: The lcm of two number a and b is given by
lcm(a,b) = ab/(GCD(a, b)), this implies ab = lcm(a, b) * gcd(a, b).

7. If a number is 2² x 3¹ x 5⁰ and b is 2² x 3¹ x 5¹ then hcf of a, b is?
a) 2² x 3¹ x 5¹
b) 2² x 3² x 5²
c) 2¹ x 3¹ x 5⁰
d) 2² x 3² x 5⁰

Answer: c
Clarification: Hcf is the product of sets having least exponent value among a and b.

8. State whether the given statement is True or False.

HCF (a, b, c, d) = HCF(a,(HCF(b,(HCF(c, d)))).

a) True
b) False

Answer: a
Clarification: HCF function can be reursively defined.

9. HCF(a, b) is equals to _________
a) ab/(LCM(a, b))
b) (a + b)/(LCM(a, b))
c) (LCM(a, b))/ab
d) None of the mentioned

Answer: a
Clarification: ab = lcm(a, b)*hcf(a, b), which implies
HCF(a,b) = ab/(LCM(a, b)).

10. The HCF of two prime numbers a and b is _________
a) ^a⁄_b
b) ab
c) a + b
d) 1

Answer: d
Clarification: Since they doesnot have any factor in common other than 1.