# What multiplies to 42?

#### Understand the Problem

The question is asking for the factors of the number 42, meaning we need to identify which pairs of numbers multiply together to result in 42.

1, 2, 3, 6, 7, 14, 21, 42

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.

#### Steps to Solve

1. Identify the Range of Factors To find the factors of 42, we need to check numbers from 1 up to the square root of 42. The approximate square root is $\sqrt{42} \approx 6.4$, so we will check all integers from 1 to 6.

2. Check for Divisibility For each integer in the range, we will check if it divides 42 evenly. If it does, both the integer and the result from dividing 42 by that integer are factors.

3. Calculate Factors

• For $1$: $42 \div 1 = 42$ (factors are 1 and 42)
• For $2$: $42 \div 2 = 21$ (factors are 2 and 21)
• For $3$: $42 \div 3 = 14$ (factors are 3 and 14)
• For $4$: $42 \div 4$ does not result in an integer, so 4 is not a factor.
• For $5$: $42 \div 5$ does not result in an integer, so 5 is not a factor.
• For $6$: $42 \div 6 = 7$ (factors are 6 and 7)
1. Compile All Unique Factors Now we compile all unique factors found: 1, 2, 3, 6, 7, 14, 21, and 42.

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.