# Factors of 36

#### Understand the Problem

The question is asking for the factors of the number 36, which means we need to identify all integers that can be multiplied together to produce 36.

The factors of 36 are $1, 2, 3, 4, 6, 9, 12, 18, 36$.

The factors of the number 36 are $1, 2, 3, 4, 6, 9, 12, 18, 36$.

#### Steps to Solve

1. Identify potential factors We need to find integers that can multiply together to yield 36. Start by considering numbers from 1 up to the square root of 36, since factors come in pairs.

2. List pairs of factors Check each integer from 1 to 6 (since $\sqrt{36} = 6$) to see if it divides 36 evenly (i.e., with no remainder).

• For $1$: $36 ÷ 1 = 36$ → Factors: $(1, 36)$
• For $2$: $36 ÷ 2 = 18$ → Factors: $(2, 18)$
• For $3$: $36 ÷ 3 = 12$ → Factors: $(3, 12)$
• For $4$: $36 ÷ 4 = 9$ → Factors: $(4, 9)$
• For $6$: $36 ÷ 6 = 6$ → Factors: $(6, 6)$ (this is a repeated factor)
3. Compile the complete list of unique factors From the pairs identified, compile a list of all unique factors:

From pairs: $1, 36, 2, 18, 3, 12, 4, 9, 6$

4. Order the factors Sort the factors in ascending order:

The ordered list of factors: $1, 2, 3, 4, 6, 9, 12, 18, 36$

The factors of the number 36 are $1, 2, 3, 4, 6, 9, 12, 18, 36$.

Factors are important in both number theory and practical applications, such as simplifying fractions or calculating least common multiples. The factors of a number can provide insights into its properties, such as whether it is prime.

#### Tips

• Miscounting factors by not considering the pairs correctly.
• Forgetting to include 1 and the number itself as factors.
• Overlooking repeated factors (like in the case of the number 6).
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