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Factors of 42

 

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 factors of a number are finite. It means, universally, that number will have a particular number of factors only.
  • Composite numbers can only be factored in because they are made from the product of two or more numbers.
  • Only integers and whole numbers can be factored in and will have factors.
  • Every factor of a number is equal to less than the number itself.

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

How to find the factors of 42?

The factors of 42 can be found by two methods –Long-division method and Prime factorization method.

Prime factorization method to find factors of 42

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-

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  • With the help of divisibility rules, we need to find out the smallest factor of the given number. Here, we have 42, which is an even number. It is divisible by 2. In other words, we can divide 42 by 2 leaving no remainder. The quotient will be 21 after performing division on 42 by 2.
  • 2 is the smallest prime factor that divides 42.
  • We can see the sum of 42 = 6. From the divisibility rule for number 3, we can find that it may be divisible by 3. 3 divides the number 42.
  • 42 ÷ 3 = 14. We need to repeat the steps with other numbers until we get the remainder of 0.
  • 14 can be divided into two more parts, i.e. 7 and 2, which are not further divisible.
  • 14 ÷ 2 = 7, and 7 ÷ 7 = 1. Here, we get remainder 1. After this, our process is completed, and we get factors of 42.

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.

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