What is the least number that should be added to 91 so that the result is coprime with 60?
6
Two numbers are coprime when their HCF is 1. Since 60 = 22 × 3 × 5, the result must not be divisible by 2, 3 or 5.
Note that 91 = 7 × 13 has no factor 2, 3 or 5, so 91 by itself is already coprime with 60; since the question asks for a number that must actually be added, we look for the least positive (natural) number whose sum with 91 is still coprime with 60.
Test the sums in increasing order of the number added: 91 + 1 = 92 (even), 91 + 2 = 93 (divisible by 3), 91 + 3 = 94 (even), 91 + 4 = 95 (divisible by 5), 91 + 5 = 96 (even).
91 + 6 = 97, which is a prime number and is not divisible by 2, 3 or 5, so HCF(97, 60) = 1.
Therefore the least natural number to be added is 6.
Check: 97 is odd, its digit sum 16 is not a multiple of 3, and it does not end in 0 or 5; so 97 and 60 share no common factor other than 1.
Hence, 6.
Similar Questions
How many numbers from 1 to 30 are coprime with 30?
The product of two consecutive prime numbers is 437. The difference between these two prime numbers is:
The sum of prime numbers upto 75 is:
Important Questions from Multiples and Factors
Express 486 as a product of powers of prime factors.
Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression \(\frac{p-q-1}{r-s}\) is:
Find the greatest three-digit number which is a multiple of 8.
The sum of three consecutive multiples of 7 is 840. The smallest of these multiples is:
If 2160 = 2 a × 3 b × 5 c , then the value of 3 a × 2 -b × 5 -c will be –
