Solved on Feb 26, 2024
Determine if any two natural numbers have at least one common factor. True or False?
STEP 1
Assumptions
1. Natural numbers are positive integers starting from 1.
2. A common factor of two numbers is a number that divides both of them without leaving a remainder.
3. The statement to evaluate is: "Any two natural numbers have at least one common factor."
STEP 2
Consider the definition of a natural number and the concept of a factor.
STEP 3
Recall that the number 1 is a factor of every natural number because every natural number is divisible by 1 without leaving a remainder.
STEP 4
Since 1 is a common factor of all natural numbers, any two natural numbers will always have at least the number 1 as a common factor.
STEP 5
Based on the above reasoning, we can conclude that the statement "Any two natural numbers have at least one common factor" is true because they all have at least the number 1 as a common factor.
The correct answer is True.
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