Many pairs of numbers, both positive and negative, multiply together to equal 60. This involves identifying the factors of 60.
Factors are numbers that divide another number exactly, leaving no remainder. When you're looking for "what multiplied by what equals 60," you're essentially seeking pairs of factors whose product is 60.
Positive Integer Factors of 60
To find all positive integer pairs that multiply to 60, we list all the positive integers that divide 60 evenly. These are also known as the divisors of 60.
Here are the pairs of positive integers that multiply to 60:
| Factor 1 | Factor 2 | Product |
|---|---|---|
| 1 | 60 | 60 |
| 2 | 30 | 60 |
| 3 | 20 | 60 |
| 4 | 15 | 60 |
| 5 | 12 | 60 |
| 6 | 10 | 60 |
The individual positive factors of 60, listed in ascending order, are:
- 1
- 2
- 3
- 4
- 5
- 6
- 10
- 12
- 15
- 20
- 30
- 60
Negative Integer Factors of 60
It's also important to remember that the product of two negative numbers is a positive number. Therefore, pairs of negative integers can also multiply to 60.
Here are the pairs of negative integers that multiply to 60:
| Factor 1 | Factor 2 | Product |
|---|---|---|
| -1 | -60 | 60 |
| -2 | -30 | 60 |
| -3 | -20 | 60 |
| -4 | -15 | 60 |
| -5 | -12 | 60 |
| -6 | -10 | 60 |
Beyond Whole Numbers
While the question typically implies integers, it's worth noting that if you consider non-integer numbers (like fractions or decimals), there are an infinite number of pairs that could multiply to 60. For example:
- 0.5 × 120 = 60
- 7.5 × 8 = 60
- √36 × 10 = 60
Understanding Factors and Multiples
Understanding factors is fundamental in mathematics, particularly in areas like prime factorization, finding common factors, and simplifying fractions. A factor of a number divides it evenly, while a multiple is the result of multiplying a number by an integer. You can explore more about factors and their properties on educational platforms such as Maths Is Fun.
