If the HCF of three numbers is 1, which of the following can be true?

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Question: If the HCF of three numbers is 1, which of the following can be true?

Options:

Correct Answer: All three numbers are prime

Solution:

If the HCF is 1, it is possible that all three numbers are prime, as they would not share any common factors.

If the HCF of three numbers is 1, which of the following can be true?

If the HCF of three numbers is 1, which of the following can be true?

Step 1: Understand what HCF means. HCF stands for Highest Common Factor, which is the largest number that divides all the given numbers without leaving a remainder.
Step 2: If the HCF of three numbers is 1, it means that there are no common factors among the three numbers other than 1.
Step 3: Recognize that prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.
Step 4: If all three numbers are prime, they cannot share any factors other than 1, which means their HCF would be 1.
Step 5: Conclude that it is possible for all three numbers to be prime if their HCF is 1.

Highest Common Factor (HCF) – The HCF of a set of numbers is the largest number that divides all of them without leaving a remainder. If the HCF is 1, it indicates that the numbers are coprime, meaning they do not share any common factors other than 1.
Prime Numbers – Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. If all three numbers are prime, their HCF will also be 1.