Question

If the HCF of the smallest odd prime number and the greatest 2-digit number is expressed as 3^m . 11ⁿ, then the values of m and n respectively are:

विकल्प

• 0, 0

• 1, 0

• 1, 1

• 2, 1

Answer 1

1, 0

Explanation:

1. Identify the numbers

Smallest odd prime number: The sequence of prime numbers is 2, 3, 5, 7, .... Since 2 is even, the smallest odd prime number is 3.

Greatest 2-digit number: The largest number with only two digits is 99.

2. Calculate the HCF

Find the Highest Common Factor (HCF) of 3 and 99:

The factors of 3 are 1, 3.

The factors of  99 are 1, 3, 9, 11, 33, 99.

The common factors are 1 and 3, so the HCF is 3.

3. Determine the values of m and n

HCF can be expressed in the form 3^m . 11ⁿ.

We equate the HCF to this expression:

3 = 3^m . 11ⁿ 

Since 11⁰ = 1 and 3¹ = 3, we can rewrite 3 as:

3¹ . 11⁰ = 3^m . 11ⁿ

By comparing the exponents of like bases:

m = 1

n = 0

The values of m and n are 1 and 0 respectively.