What are the factor pairs for 60
The Correct Answer and Explanation is:
Correct Answer:
The factor pairs of 60 are:
(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)
Explanation
Factor pairs are two numbers that multiply together to give a specific product. In this case, the goal is to find all the pairs of positive integers that, when multiplied, equal 60. Each pair consists of two factors such that the product of the two is exactly 60.
To determine these pairs, start by identifying the smallest positive integer, which is 1. Multiply 1 by 60 to get 60. This gives the first pair: (1, 60). Next, try 2. Since 60 divided by 2 equals 30, (2, 30) is a valid pair. Continue this process:
- 3 × 20 = 60 → (3, 20)
- 4 × 15 = 60 → (4, 15)
- 5 × 12 = 60 → (5, 12)
- 6 × 10 = 60 → (6, 10)
At this point, the next number would be 7, but 60 divided by 7 results in a decimal, not a whole number. This indicates that 7 is not a factor of 60. Continue checking numbers until reaching a point where the first number in the pair is greater than the second. At that point, all possible factor pairs have been listed.
The reason this method works is based on the property of multiplication being commutative—meaning the order of the factors does not affect the product. Therefore, once the smaller number in the pair becomes larger than the other, the list starts repeating in reverse.
Factor pairs are especially useful in problem-solving related to area, number theory, or simplifying fractions. They show how a number can be broken down into parts and are a foundation for understanding greatest common factors, least common multiples, and prime factorization.
