1. Steps to find factors of 28 using Division Method

Example: Find factors of 28

  • Divide 28 by 1: 28 ÷ 1 : Remainder = 0
  • Divide 28 by 2: 28 ÷ 2 : Remainder = 0
  • Divide 28 by 4: 28 ÷ 4 : Remainder = 0
  • Divide 28 by 7: 28 ÷ 7 : Remainder = 0
  • Divide 28 by 14: 28 ÷ 14 : Remainder = 0
  • Divide 28 by 28: 28 ÷ 28 : Remainder = 0

Hence, Factors of 28 are 1, 2, 4, 7, 14, and 28

2. Steps to find factors of 28 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 28 using the division method, follow these steps:

  • Step 1. Start dividing 28 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 28, which is 2. Divide 28 by 2 to obtain the quotient (14).
    28 ÷ 2 = 14
  • Step 3. Repeat step 1 with the obtained quotient (14).
    14 ÷ 2 = 7
    7 ÷ 7 = 1

So, the prime factorization of 28 is, 28 = 2 x 2 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 28 as shown below:

So, the prime factorization of 28 is, 28 = 2 x 2 x 7.

3. Find factors of 28 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 28 would be the two numbers which, when multiplied, give 28 as the result.

The following table represents the calculation of factors of 28 in pairs:

Factor Pair Pair Factorization
1 and 28 1 x 28 = 28
2 and 14 2 x 14 = 28
4 and 7 4 x 7 = 28

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 28. They are called negative pair factors.

Hence, the negative pairs of 28 would be ( -1 , -28 ) , ( -2 , -14 ) and ( -4 , -7 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 28 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 28.
  • Every number is a factor of zero (0), since 28 x 0 = 0.
  • 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, 4, 7, 14, 28 are exact divisors of 28.
  • Factors of 28 are 1, 2, 4, 7, 14, 28. Each factor divides 28 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 28 are all less than or equal to 28.

Frequently Asked Questions

  • What are the prime factors of 28?

    The factors of 28 are 1, 2, 4, 7, 14, 28.
    Prime factors of 28 are 2, 2, 7.

  • What is the sum of all factors of 28?

    The sum of all factors of 28 is 56.

  • What are the pair factors of 28?

    Pair factors of 28 are (1,28), (2,14), (4,7).

  • What two numbers make 28?

    Two numbers that make 28 are 2 and 14.

  • What are multiples of 28?

    First five multiples of 28 are 56, 84, 112, 140.

  • Is 28 a perfect square?

    No 28 is not a perfect square.

  • Which is greatest factor of 28?

    The greatest factor of 28 is 14.

  • How do you factors of 28?

    Factors of 28 are 1, 2, 4, 7, 14, 28.

  • What are five multiples of 28?

    First five multiples of 28 are 56, 84, 112, 140, 168.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 28?

Factors of 28 are 1, 2, 4, 7, 14, 28.
Even factors of 28 are 2, 4, 14, 28.
Hence, product of even factors of 28 is; 2 x 4 x 14 x 28 = 3136.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 28? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 14, 28.
Negative factors are -1, -2, -4, -7, -14, -28.

How many factors are there for 28?

Factors of 28 are 1, 2, 4, 7, 14, 28.
So there are in total 6 factors.

Sammy is puzzled while calculating the prime factors of 28. Can you help him find them?

Factors of 28 are 1, 2, 4, 7, 14, 28.
Prime factors of 28 are 2, 2, 7

Joey wants to write all the prime factors of 28 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 28 are 2, 2, 7.
So in exponential form it can be written as 22 x 7.

What is prime factorization of 28?

Prime factorization of 28 is 2 x 2 x 7 = 22 x 7.

Can you help Rubel to find out the product of the even factors of 28?

Factors of 28 are 1, 2, 4, 7, 14, 28.
Even factors of 28 are 2, 4, 14, 28.
Hence, product of even factors of 28 is; 2 x 4 x 14 x 28 = 3136.