What are the factor pairs for 60
The Correct Answer and Explanation is:
Factor Pairs of 60:
The factor pairs of 60 are:
(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)
Explanation:
A factor pair consists of two numbers that multiply together to give a specific product. In this case, the goal is to identify all the pairs of whole numbers whose product equals 60.
To begin, 1 and 60 are factor pairs because 1 × 60 equals 60. Increasing the smaller number step by step helps to find the rest. The next pair, 2 and 30, satisfies the condition because 2 × 30 gives 60. Similarly, 3 and 20 form another pair due to 3 × 20 equaling 60. Continuing this approach, 4 × 15 equals 60, forming the next valid pair. The number 5 also works, since 5 × 12 equals 60. Lastly, 6 and 10 also meet the requirement because 6 × 10 equals 60.
After reaching the point where the first number in the pair is equal to or exceeds the square root of 60 (which is approximately 7.75), the search can stop. Any further multiplication involving larger first numbers would duplicate earlier results but in reverse order, which do not count as new pairs in factor pair listings.
Identifying factor pairs proves useful in arithmetic, algebra, and problem-solving contexts. They aid in simplifying fractions, solving equations, and understanding number properties. Factor pairs also provide insights into the structure of a number, such as whether it is prime or composite. In this case, since multiple factor pairs exist for 60, it confirms that 60 is a composite number. Each of the pairs shows a different way in which 60 can be broken down into the product of two natural numbers.
