Question

A and B are the largest two-digit co-prime numbers and all the digits are co-prime to one another. If the largest one is divided by the smallest one, the remainder is 
1. Even prime number
2. Odd prime number 
3. Not a prime number
4. Can’t be determined

Answer 1

Correct Answer - Option 2 : Odd prime number 

Formula Used:

Remainder Theorem

Dividend = (Divisor × Quotient) + Remainder           

Concept Used:

Any set of numbers that do not have any common factor other than 1 are called co-prime or relatively prime numbers.

Calculation:

Largest two-digit co-prime numbers = 99, 98

But digits of 99 are not co-prime to each other.

We consider 98 and 75 both are co-prime and all the digits of each number are co-prime to one another.

Let A = 98 and B = 75

98 = 75 × 1 + 23

When the bigger one is divided by the smaller one, the remainder is 23

∴ 23 is an odd prime number.