What numbers go into 42?

Understand the Problem

The question is asking for the factors of the number 42, meaning we need to identify which numbers can be multiplied together to yield 42.

Answer

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

Steps to Solve

Identify potential factors Begin by listing all integers starting from 1 up to half of 42, since any factor larger than half cannot be a factor of 42. The potential factors are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
Check divisibility of each number For each potential factor, check if it divides 42 evenly (i.e., with no remainder). We can do this by performing the division and checking if the result is an integer.
List confirmed factors The factors of 42 are those numbers that divide 42 evenly. For example:

$42 \div 1 = 42$ (1 is a factor)
$42 \div 2 = 21$ (2 is a factor)
$42 \div 3 = 14$ (3 is a factor)
$42 \div 6 = 7$ (6 is a factor)

Compile all factors After checking each number, compile a complete list of all the factors found.

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

More Information

The number 42 is a composite number, meaning it has more factors than just 1 and itself. It is the product of the prime factors $2 \times 3 \times 7$. Factors can be helpful in various mathematical concepts, including fractions and simplifications.

Tips

Forgetting to consider 1 and the number itself as factors. Always remember that every integer has 1 and itself as factors.
Not checking all integers up to $n/2$. If a factor is larger than half the original number, it won't be a valid factor unless it is the number itself.

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