The numbers that equal 36 in multiplication are its factor pairs, which include (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).
These pairs represent all the positive integer combinations that multiply together to yield 36. Finding these pairs is a fundamental concept in mathematics, often explored when learning about factors and multiples.
As detailed by sources like Socratic.org, the complete set of positive integer pairs that multiply to 36 are:
| Factor 1 | Factor 2 | Product |
|---|---|---|
| 1 | 36 | 36 |
| 2 | 18 | 36 |
| 3 | 12 | 36 |
| 4 | 9 | 36 |
| 6 | 6 | 36 |
Understanding Factors of 36
A factor of a number is an integer that divides the number without leaving a remainder. When we talk about "numbers that equal 36 in multiplication," we are referring to these factor pairs. The individual positive factors of 36 are:
- 1
- 2
- 3
- 4
- 6
- 9
- 12
- 18
- 36
How These Factors Are Found
Typically, to find all factors, one starts testing division from 1 upwards. If a number divides 36 evenly, both the divisor and the quotient are factors. This process continues until the divisors meet or exceed the square root of 36 (which is 6), ensuring all pairs are found without duplication. For instance, after finding 6 × 6, any subsequent factors would just be reversals of pairs already found (e.g., 9 × 4, which is the same pair as 4 × 9).
