1. Steps to find factors of 42 using Division Method

Example: Find factors of 42

  • Divide 42 by 1: 42 ÷ 1 : Remainder = 0
  • Divide 42 by 2: 42 ÷ 2 : Remainder = 0
  • Divide 42 by 3: 42 ÷ 3 : Remainder = 0
  • Divide 42 by 6: 42 ÷ 6 : Remainder = 0
  • Divide 42 by 7: 42 ÷ 7 : Remainder = 0
  • Divide 42 by 14: 42 ÷ 14 : Remainder = 0
  • Divide 42 by 21: 42 ÷ 21 : Remainder = 0
  • Divide 42 by 42: 42 ÷ 42 : Remainder = 0

Hence, Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42

2. Steps to find factors of 42 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 42 using the division method, follow these steps:

  • Step 1. Start dividing 42 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 42, which is 2. Divide 42 by 2 to obtain the quotient (21).
    42 ÷ 2 = 21
  • Step 3. Repeat step 1 with the obtained quotient (21).
    21 ÷ 3 = 7
    7 ÷ 7 = 1

So, the prime factorization of 42 is, 42 = 2 x 3 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 42 as shown below:

So, the prime factorization of 42 is, 42 = 2 x 3 x 7.

3. Find factors of 42 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 42 would be the two numbers which, when multiplied, give 42 as the result.

The following table represents the calculation of factors of 42 in pairs:

Factor Pair Pair Factorization
1 and 42 1 x 42 = 42
2 and 21 2 x 21 = 42
3 and 14 3 x 14 = 42
6 and 7 6 x 7 = 42

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 42. They are called negative pair factors.

Hence, the negative pairs of 42 would be ( -1 , -42 ) , ( -2 , -21 ) , ( -3 , -14 ) and ( -6 , -7 ) .

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 42 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 6, 7, 14, 21, 42 are exact divisors of 42.
  • 1 is a factor of every number. Eg. 1 is a factor of 42.
  • Every number is a factor of zero (0), since 42 x 0 = 0.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -42 )?

    Factors of -42 are -1, -2, -3, -6, -7, -14, -21, -42.

  • What is the sum of all factors of 42?

    The sum of all factors of 42 is 96.

  • What is prime factorization of 42?

    Prime factorization of 42 is 2 x 3 x 7.

  • What are the pair factors of 42?

    Pair factors of 42 are (1,42), (2,21), (3,14), (6,7).

  • What are six multiples of 42?

    First five multiples of 42 are 84, 126, 168, 210, 252, 294.

  • Is 42 a whole number?

    Yes 42 is a whole number.

  • Which is the smallest prime factor of 42?

    Smallest prime factor of 42 is 2.

  • What are five multiples of 42?

    First five multiples of 42 are 84, 126, 168, 210, 252.

  • Write all factors of 42?

    Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

Examples of Factors

Joey wants to write all the prime factors of 42 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 42 are 2, 3, 7.
So in exponential form it can be written as 2 x 3 x 7.

How many factors are there for 42?

Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 42. Can you predict the answer?

7 factor(s) of 42 are 1, 2, 3, 6, 7, 14, 21.

Sammy is puzzled while calculating the prime factors of 42. Can you help him find them?

Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.
Prime factors of 42 are 2, 3, 7

What is prime factorization of 42?

Prime factorization of 42 is 2 x 3 x 7 = 2 x 3 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 42. Can you help her?

Prime factors of 42 are 2, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 42?

Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.
Even factors of 42 are 2, 6, 14, 42.
Hence, product of even factors of 42 is; 2 x 6 x 14 x 42 = 7056.