What numbers multiply to 36?
Understand the Problem
The question is asking for the numbers that can be multiplied together to yield the product 36. This involves identifying pairs of factors of the number 36.
Answer
The pairs of factors of 36 are $(1, 36)$, $(2, 18)$, $(3, 12)$, $(4, 9)$, and $(6, 6)$.
Answer for screen readers
The pairs of numbers that multiply together to give 36 are:
- $(1, 36)$
- $(2, 18)$
- $(3, 12)$
- $(4, 9)$
- $(6, 6)$
Steps to Solve
- Identify the factors of 36
To find the pairs of numbers that can be multiplied to yield 36, start by listing all the factors of the number 36. The factors are integers that divide 36 without leaving a remainder.
- List the pairs of factors
Once you have all the factors, pair them up such that the product of each pair equals 36. For each factor $f$, its pair can be found by calculating $p = \frac{36}{f}$.
- Compile the complete list of factor pairs
Collect all the pairs of factors you have found. For example, if one factor is 1, its pair would be 36, since $1 \times 36 = 36$. Do this for all factors.
The pairs of numbers that multiply together to give 36 are:
- $(1, 36)$
- $(2, 18)$
- $(3, 12)$
- $(4, 9)$
- $(6, 6)$
More Information
The number 36 is a composite number, which means it has factors other than 1 and itself. Notably, in this case, one of the pairs is $(6, 6)$, indicating that $6$ is a perfect square factor.
Tips
- Forgetting to include both members of a factor pair, which can lead to an incomplete list.
- Not realizing that factors need to be integers.
- Confusing factors with multiples; factors are what can be multiplied together to reach the number, while multiples result from multiplying a number by integers.
