Given below are two statements: Statement I: Co-primes are the numbers which…
2020
Given below are two statements:
Statement I: Co-primes are the numbers which have only 1 as their common factor.
Statement II: Factorisation is the decomposition of a number into the other numbers which when added together will give the original number.
In the light of the above statements, choose the correct answer from the options given below:
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
Attempted by 58 students.
Show answer & explanation
Correct answer: C
Concept
Two numbers are called co-prime (relatively prime) when the only positive integer that divides both of them is 1; equivalently, their greatest common divisor (GCD) equals 1.
Factorisation is the process of expressing a number as a product of other numbers (its factors); the original number is recovered by MULTIPLYING those factors together, not by adding them.
Applying it to each statement
Statement I describes co-primes as numbers whose only common factor is 1. This is exactly the definition of co-prime numbers, so Statement I is true.
Statement II says factorisation decomposes a number into other numbers that ADD up to the original. Factorisation is about a PRODUCT of factors, not a sum, so Statement II is false.
Cross-check with a concrete number
Take 12. Its factorisation is 12 = 2 x 2 x 3, where the factors multiply to give 12 (note 2 + 2 + 3 = 7, not 12) — confirming Statement II's 'added together' wording is wrong. Also 8 and 15 share no common factor except 1, so they are co-prime — confirming Statement I.
Therefore the correct conclusion is: Statement I is correct but Statement II is false.