This set of Discrete Mathematics Questions and Answers for Campus interviews focuses on “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

View Answer

Explanation: 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

View Answer

Explanation: 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

View Answer

Explanation: 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

View Answer

Explanation: 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

4) None of the mentioned

View Answer

Explanation: 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

View Answer

Explanation: 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 2^{2} x 3^{1} x 5^{0} and b is 2^{2} x 3^{1} x 5^{1} then hcf of a, b is:

a) 2^{2} x 3^{1} x 5^{1}

b) 2^{2} x 3^{2} x 5^{2}

c) 2^{1} x 3^{1} x 5^{0}

d) 2^{2} x 3^{2} x 5^{0}

View Answer

Explanation: 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

View Answer

Explanation: 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

View Answer

Explanation: 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

View Answer

Explanation: Since they doesnot have any factor in common other than 1.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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