The alternate numbers are always co-prime numbers.

True

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False

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Solution

The correct option is B
False

According to the concept of co-prime numbers, two numbers have to be consecutive numbers but not alternate numbers for being co-prime. Alternate numbers are either odd numbers or even numbers and hence will have a common factor greater than one. The HCF of co-prime numbers is always 1, as there is nothing common apart from 1. Consider any consecutive numbers like 4, 5 or 10, 11. The number which is common between all these pairs is 1. So our statement is false. The correct one is that the consecutive numbers are always co-prime numbers.

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Similar questions

State true (T) of false (F):

$(i)$ The sum of primes cannot be a prime.

$(i i)$ The product of primes cannot be a prime.

$(i i i)$ An even number is composite.

$(i v)$ Two consecutive numbers cannot be both primes.

$(v)$ Odd numbers cannot be composite.

$(v i)$ Odd numbers cannot be written as sum of primes.

$(v i i)$ A number and its successor are always co-primes.

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