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We can define the factors of 42 as the numbers that divide 42 leaving no remainder. This means, 42 must be completely divisible by such a number that it does not leave any remainder.
The integer 42 can be divided only into three numbers – 2, 3, and 7. It means, the product of 2, 3, 7 will result in number 42.
Moreover, the number 42 will have the following factors: 1, 2, 3, 6, 7, 14, 21, and 42.
Therefore, the largest factor of 42 is 21, which is a composite number. The largest prime factor of 42 is 7. The number 42 can be written as: 42 = 2 x 3 x 7.
However, 42 will have the following categories of factors-
Positive factors: 1, 2, 3, 6, 7, 14, 21, and 42.
Prime factors: 1, 2, 3, 7
Negative factors: -2, -3, -6, -7, -14, -21, and -42.
Prime factorization of 42 = 2 x 3 x 7
The factors of 42 can be found by two methods –Long-division method and Prime factorization method.
The prime factorization method is the most common method to represent several numbers, including 42. Prime factorization also has another form, the prime factor tree method, which is a visual method to represent factors of 42. It helps in determining various prime factors of 42. A factor tree is not unique for a given number. Instead of expressing 42 as 21 x 2 or 6 x 7, we can represent 42 as 2 x 3 x 7.
We need to divide 42, from the smallest number to the largest number so that it completely divides the number-
Prime factorization of 42 using the prime factorization method is 2 x 3 x 7.
Example 1: What are the common factors of 42 and 48?
Solution: The factors of 42 are 2, 3 and 7. The factors of 48 are 2, 3, 4, 6, 8, 12, 18, and 24. Thus, the common factors of 42 and 48 are: 2 and 3 only.