Grade 10 Maths Real Numbers Quiz (Part A)

If p and q are two distinct prime numbers, then their HCF is

• 2

• 0

• either 1 or 2

• 1

Answer explanation

SOLUTION A prime number has no factor other than 1 and the number itself. Therefore, Factors of p are: 1 and p only. Factors of q are: 1 and q only. Therefore, 1 is the only common factor of p and q. Hence, HCF (p, q) = 1.

If p and q are two distinct prime numbers, then LCM (p, q) is

• 1

• p

• q

• pq

Answer explanation

Solution

Let p be a prime number. The sum of its factors is

• p

• 1

• p + 1

• p - 1

Answer explanation

SOLUTION The factors of p are 1 and p. So, their sum is p + 1.

Let p be a prime number. The quadratic equation having its factors as zeros is

Answer explanation

The LCM of the smallest two digit composite number and the smallest composite number is

• 12

• 20

• 4

• 44

Answer explanation

The HCF of smallest prime number and the smallest composite number is

• 2

• 4

• 6

• 8

Answer explanation

SOLUTION The smallest prime and the smallest composite numbers are 2 and 4 respectively.

HCF (2,4)=2.

The smallest number divisible by all natural numbers between 1 and 10 (both inclusive) is

• 2020

• 2520

• 1010

• 5040

Answer explanation

The HCF of two consecutive positive integers is

• 0

• 1

• 4

• 2

Answer explanation

SOLUTION In any two consecutive positive integers one is even and other is odd. So, they have 1 as the only common factor. Hence, their HCF is 1.

Let n be a natural number. Then, the LCM (n, n + 1) is

• n

• n + 1

• n (n + 1)

• 1

Answer explanation

SOLUTION For any natural number n, natural numbers n and n + 1 are relatively prime.

:.

LCM (n, n+1)= n(n+1).

If m=dn + r where m, n are positive integers and d and r integers, then n is the HCF of m and n, if

• r = 1

• r = 0

• r is a real number

Answer explanation

If n is the HCF of m and n, then n is a factor of m and hence n is a factor of dn + r. This is possible only when r=0.